Hi,
I agree with other posters that you will be really strapped with a 2.5k rent. Moreover, you will be completely dependent on your soon-to-be ex holding up their part of the bargain. If they flake, you sink. So I would first like to question your assumptions.
Could you deal with a one bedroom place? Depending on the age of your kids it might be doable.
You didn't give us any details about the city/town where you live, but I wonder whether you could move just outside the really expensive area. Since you already have a car, you might be able to save a bunch of money and still be close enough.
Why not do yard work? If I were you I'd be looking for someone who wants to have more than just a tenant (e.g. an older person who might be willing to offer a steep discount on rent in exchange for help with yardwork/errands/etc). Being creative could help you avoid a financially difficult situation.
OK, having posed questions, here is my advice on finding a good landlord. Look for an individual who really cares about their property and who has a good track record with their tenants. In my (long) rental career, I learned to avoid corporate management companies of any kind like the plague. They nickel and dime tenants and raise rents to monetize the agony of moving (which, with kids, will be large). If you present yourself as a responsible individual who will do your best to care for their property you can find someone who will pay you (in the form of fewer rent hikes, etc) for being a good tenant. I would be very clear about what they expect of you and what they will do for you. You can ask specific questions about how they handle maintenance issues, etc. You can also offer specifics about what you will do (e.g. care for the place, keep quiet between X and Y hours, etc).
Good luck!