Get a copy of the records ( any bloodwork, Xrays, ultrasound results) So the new vet can have a good place to start. Maybe look for a feline only veterinarian and/or a board certified specialist
at a specialty practice.
Good Luck
Usually most vets like to wait anywhere from 2 to 4 weeks after the kittens are weaned to spay the queen. ( It depends on which one of us you talk to -lol.)
The fact that she is very visibly pregnant means that she could have the kitties at any time now. Average gestation is approximately 63 days.
Kittens can be weaned at 5 to 6 weeks of age. They definitely should be able to rehomed by 8 or 9 weeks. It us advisable to get their first check up at the vets by 8 weeks for their first vaccine +/- their feline leukemia test. Good luck.