I have a writ of execution against me and they froze my bank account. It is a joint account with a father inlaw on it, the judgement is just on me and not him. Will I be able to get the bank account unfroze.

Generally speaking, the only way to get the bank account unfroze is to satisfy the judgment. And whomever it is that got the judgment against you might not be satisfied until paid in full. When the bank receives the court order, they have to comply and do as instructed for however long they're being told to do so. As with joint account holders and a judgment, I do suggest that your father in law should open a separate accout in his name only and direct his source of funds to it. If there are exempt funds in this frozen account and/or you're trying to keep your father in law's fund safe, you will have to challenge the judgment. But that is a very arduous task. And you will need to be able to prove that. The only one who can get the judgment removed is the same one who petitioned the court to put it on there.

Your father in law, can file with the court, and prove which of the funds are his, and he can get his money back, but the account itself would remain frozen of all of your money in there

The fact that the judgment is just against you us immaterial. As long as you are listed as an owner of the account, its fair game for attachment.

As noted your father in law can try going to court and asking for a release against his funds IF he can prove which were his.