Does she ever hang out with your family when you aren't there? Do they have anything in common you could exploit? Like common interests in music that you can send them together to a concert?

It sounds like this problem has been going on for a very long time and there may be deeper issues. If it's really that she is just shy and uncomfortable, it might be a matter of just breaking the pattern and getting her to enjoy their company.

If it's something deeper, it might help her to just describe how she's feeling and why she thinks she might be feeling that way around them. Is she afraid if she says the wrong thing your family will hate her and you two will separate? Is she jealous of them somehow? It may take some patience to find out what is bothering her, but it might solve your problem.

Failing all that ... Marriage counseling is your friend

Good luck to ya!