The rented a house in Florida in July of this year. The aunt got mad at him and moved back to Texas. She told him she can come and go as she pleases. My son talked to the landlord, he said that was a family issue and not his. What right does my son have? Does he have rights if she does not pay her part?
Can she be removed from the lease? Please let me know your thoughts.

If he and she are both on the lease, then each person is liable for the entire amount, and any grievance is between the two of them. So the landlord is correct about that - he doesn't have to chase down each person for half. Now technically your son cannot just tell the landlord to take her off the lease. But the LL can terminate both of them for non payment and then rent to your son, which should be easier if she doesn't show up for quite a while. Your son would negotiate a deal to cover the amount not paid retroactively after the LL terminates. A sort of staged eviction.

The landlord is correct, he may attempt to sue her for 1/2 of the rent if he wants, but he has to pay it. Unless she will sign a release to allow son to sign a new lease ( if landlord even would) if son for example, stopped paying rent, he and aunt can both be sued, even if she moved.