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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
You're allowed to rely upon his statement that he's not going to move in and start looking for another renter. I realize that it might be difficult to find someone this time of year, but you're required to make reasonable efforts by advertising the place for a similar price. If you're not able to find a new tenant by the time you go away, then you can sue the original tenant for the money you'd have received if they had moved in like they were supposed to.
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You can actually refuse to allow her son to live there unless he signed the lease (assuming he's over 18, and it sounds like he is). You're allowed to do a credit check for him, too, and decide on your own whether you want to live there. And you can't be made to sign a new lease with the woman and her son if you don't want to (especially if they don't qualify).
At the same time, you can also hold the boyfriend responsible for his promise to pay the lease, if the other tenants are still moving in. He signed the lease, he has to make sure the rent is paid. So that's another possibility.
The only way you'd be able to re-rent the place is if the woman and her son are not moving in. You can let them know that you agreed to rent the place to BOTH tenants, and you're not going to rent the place to her alone because she doesn't qualify, unless she can give you some evidence that she has the money.
I'm sorry, but if your husband is not going to help you, there's really nothing I can tell you, other than to do the credit check on your own. As long as the two of you own the house together, you have to work together to make decisions. You can't make him break the lease with her, even if you have reason to believe she won't pay the rent.