A.V.
Friend of mine got a job in another state when she was on maternity leave. What they did was start looking for housing when their son was 1 month old and moved when he was about 3 months old. He had frequent flier miles before he was 1!
Many people also send one spouse on ahead. You stay with the kids with your MIL for a bit while he goes forward, gets some housing, moves some essentials into it, and starts his new job. Nothing says you have to sell your home IMMEDIATELY, though it might be best financial sense. I would get in touch with a realtor and let them to do the work of showing the house, etc. Take that off your mind.
I'd also enlist friends and other family to help you pack or watch the kids. Maybe get a Pod so you can move things into the Pod as you have time and then move the whole Pod when you're ready. It might also help you store things while you stage the house for sale.