I realise that it sounds odd that we want to rent the house out rather than living in it, but the idea behind that is to ensure the boys do not have any notion that they can move back in.
It seems like a drastic step to make sure the boys don't move in. Don't you think they might figure it out some day, which may cause more tension? Another option would have been to buy a house outside of that neighborhood or even in a neighboring town so there's no emotional attachment to the house. Did the boyfriend get a deal he couldn't resist on the house or was he emotionally attached to it too? How do you feel OP, about some day moving to a house that he shared with his ex for so many years? If the boys move into your rental place until their next step, make sure you explain it to the landlord first and get the clearance for that. Otherwise, it could be a problem.
Do all 3 dogs belong to the boys? If so, it won't be so easy to either move in with you temporarily or find a place that allows dogs. It's a shame people don't think before getting pets (or having kids in many cases). Did they plan on living in the house with the mother for the duration of the dogs lives, which could be another 15 years?