wa alykom as salam sister
most welcome to our small family here, Alhamdulelah we see ourselves of a family more than a forum.
as for your question, yes one is allowed to take a second haj as long as he/she completed the fard on behalf of someone else.
according to the incident during the Haj of the Messenger (PAPBUH) when a woman came asking him that her father can not be stable on a camel back in an indication of his age and health limitation. She said shall I make haj on his behalf, the messenger approved it.
And yes Insh aAllah it will count as the person performed the haj
May Allah bring ease to this family ameen
