I would definitely think about looking for some land separate to the house. So long as its fenced, and has a shed, or shelter for the goats - they will be fine. I have goats at two separate places, not near my house, and we cope.
Also, another suggestion - perhaps someone could let you use an outbuilding, couple of stables, or similar. Being winter, I am sure the goats would not mind having no field, obviously you would need to give them plenty of hay to keep them amused - but better than having to part with them. My goats are in full time now and do not seem to mind.
So sorry you are in this predicament, and hope a solution comes along soon.