Bismillah
Hello christynicole and thank you for your questions. I will try to answer to the best of my knowledge from my own understanding of what you are talking about. I hope I am not saying anything incorrect or misleading, and I do not want to make any fatawas but just to try to explain my understanding of these questions. Please, if I am wrong about any of these answers will someone correct me and inshaAllah we can all learn from these questions.
First of all, I must say both you and your husband must both be very patient and loving people to live peacefully with each other for 8 years with different beliefs! This is very nice and I am so glad you are trying to learn about Islam.
Ok, for your first question, about the hadith that says women are deficient in intelligence and religion... first let me tell you that we have to be careful about English translations of both Qur'an and hadith because they can be misleading. Here is an English translation of that hadith that you mention:
“On the occasion of Eid, either that of sacrifice or that of ending the fast, the Prophet went to the prayer place, and then went to speak to women and he said: “Ladies! ... I have not seen people deficient in mind and religion yet can get away with a rational man’s mind like any one of you.” They asked: “How are we deficient in mind and religion, Messenger of God?” He said: “Is it not true that a woman’s testimony counts as half that of a man?” When they answered in the affirmative, he said: “This is her mental deficiency. Is it not true that when a woman is in her period she neither prays nor fasts?” They again answered in the affirmative. He said: “This is her religious deficiency.” (Related by Al-Bukhari and Muslim)
This translation is from this website
http://www.islamicvoice.com/april.2003/dialogue.htm
which also offers a good interpretation of the hadith. But let me offer a summary of what I have found on this hadith.
I read about this when I was learning about Islam, and I was shocked because until then, I had only heard about the honored status of women, so how could the Prophet SAWS say women are deficient in mind and religion? Here is what I found. "Deficiency" in this case does not really mean a bad thing, as in the context in English it means something that has a fault by being deficient. But in the context used here, it means that because of women's nature, given by Allah for a good purpose, women have less responsibility in these areas, which is not a "fault" -- it is simply the way it is.
The reason that 2 women's testimony is needed to equal that of a man is because women are very loving and gentle by nature (which is needed for raising a good family) and they could have compassion for someone whom they testified against and in their own mind put them in a better light. This is why it is said 2 women are needed for one testimony, so that the other can remind her. By the way, this should be seen as a mercy for a woman, so that if she is ever called to witness on something she cannot be held solely accountable for any errors she makes. But a man, who as a human can also make errors, will be held strictly accountable for those. So you see, the woman has less responsibility in this area, and this is translated as a "deficiency."
The same holds true for the religion part. Because of the woman's cycle which is necessary for childbirth, she has regular periods where she does not pray or fast, which simply means she is responsible for less than a man in this regard. I have heard that women are encouraged to give charity to make up for what they are missing out on in terms of reward for the prayers they miss, but the way I see it if a woman has a period and does not pray, this is Allah's will and the way He designed us, and so the woman is simply following Allah's will in this and will be rewarded for her patience.
As to whether or not "modern" muslims believe women are deficient in these... it does not matter if we are modern or not, the principles of Islam apply to all people for all times. So yes, the hadith holds true today, but in the way that I have explained above. In no way does anyone think that a woman is inferior to a man because of this. Men are not allowed to restrict women from praying in the masjid, because a woman's worship is just as valid as a man's worship and she has just as much right to pray in the masjid if she wants. There are also many other instances in the Qur'an which say that men and women will receive equal reward for equal deeds. I won't quote any because I'm assuming you are aware of these. So as far as religion goes, men and women are seen as equal, but women have less required of them because of their periods and childbirth.
For intelligence, it is the same. Men and women are seen as having the same capability of knowledge and understanding, both of religion and of anything scholastic subjects. When a man is looking for a wife, he should prefer a woman who is educated, because she will be the one to raise and teach their children. Also, just as we are not allowed to restrict a woman from attending the masjid, we are not allowed to restrict a woman from gaining an education. So in all practical senses, men and women are definitely equal --- but equality does not mean SAMENESS, and men and women have different requirements and responsibilities, but the same reward for fulfilling their respective roles.
Ok I'm sorry that answer was so long, but I hope I have made it clear to you inshaAllah, and again if I have made any error please anyone correct me, and inshAllah Allah will guide us to the truth. And once again I want to make clear that my answer is only out of my own understanding.
For your second question, about the beating. This is again an issue of translation. Here is the basic point of that ayat. If a man thinks his wife might be doing something against Islam or something that would compromise the chastity of their marriage, such as maybe she doesn't pray all her prayers, or she talks too much to other men.... then he needs to correct her, both for her sake and for the sake of their marriage and family. He has three options to correct her, and they must be done in order. First he must ask her to stop. If after he asks her she continues, then he should continue to ask her but may also punish her by denying intimacy. And the Qur'an is clear in saying if he does this and she corrects her actions, then he can no longer punish her for this. If after he does these two things she still does not correct herself, then he may "beat" her. And this is the controversial word. I don't know the arabic word that is being translated (can anyone let us know?), but I understand that it should be translated as to "beat lightly" as with a small twig or toothbrush, which obviously would not hurt, but it would be a physical way to show her that she is doing the wrong thing. Kind of like if you lightly slap someone's shoulder if they do or say something you don't like. It is an immediate expression of your disapproval, and it is effective because they can feel it. But it is not intended to cause harm. In no way should a man harm his wife, either physically or emotionally. It is his responsiblity to care for her.
I should add that if you think about it, if you are in a situation with your husband where maybe there is a guy at work who always wants to take you to lunch everyday and your husband says he is jealous and does not want to you go to lunch with him... he has taken his first option and asked you to stop. If you love him, which I assume you do, and you do not want to make problems in your marriage, it's easy just stop doing it. And if there is any situation where he has to take his second or third option, then there is something wrong because you should want to please your husband and not continue doing something like this that makes problems in your marriage. In Islam, it is the wife's responsibility to keep harmony in the home, so I honestly don't think this should ever be an issue if you are married to a good person and you love each other, it should never get to the point where this is a problem.
I should also add that women are not given these options with their husbands simply because men have greater strength than women and if a husband is doing something wrong that requires correction in this manner, then he is probably not a good muslim and there is a danger that he could hurt his wife in retaliation. It is better for her to seek arbitration than to try to further provoke her husband.
But really, I have never ever heard of something like this ever happening, it seems like it would be a rare case because as I said, a husband and wife should both want only to make the marriage happy.
Again this is only from my opinion and understanding and I hope it makes things clear for you. If I have made any error, please someone correct me inshaAllah. And please anyone add something to make it more clear if you have anything inshaAllah.
Allah knows best.
salam