They might not have a smaller apartment in your facility. Ask them specifically why they want you to move to another town. Since you already have an apartment you should get priority housing. Even if the waiting list is a year or more long you have priority since they need to move you to get the 3 bedroom list down by one family. They should give you the next 2 bedroom available where you live now, within a reasonable time frame. Otherwise see if son will remain a resident until they have a two bedroom come up.
Explain transportation to schools/changing school districts will be detrimental (will your child be able to get to school? Do they ride a bus now and in that new town they don't offer that option? Does your child play sports for the school and the new one doesn't? Such things as these...)
Doctors, church congregations, travel to and from your current area things that are part of your lives, the cost of moving/gasoline/renting a truck/driving said truck along with all the other cost and stress of moving.
So many things come to mind. I'd tell them no and I would make my son stay at home until this was all sorted out so they wouldn't be able to force you to move.
If he's going off to college or getting married or something I understand but if he's just moving out on his own I'd ask him to put it off a couple of months so that you could get this sorted out. IF, IF, IF he's going off to college but this will remain his home while he's attending college then I'm not sure they can make you move. If he will be home most weekends, summer breaks, winter breaks, spring break, etc...then he is still basically living in your home and will require his own space.