We had a neighbor who left a child behind wile the family moved, but it was only for a semester. The poor girl seemed very lost, and dependent on the kindness of others to get her through.
Our family found out in late 2012 that DH would need to move (plant closing). Even with a long lead time, it was really tough. We promised DS(now)19 that he would graduate from his original HS (in 2015). It was very difficult for us, but we managed it--DH worked at his original plant until 1/15, then was transferred to another plant where he could commute home on weekends. He had originally had a great job offer, 1000 miles away, in Oct. 2014, that he very politely declined, because we felt the time frame was too long for DH being away. I hoped the company would call back in a few months--DH was very clear that he was turning them down only because of timing. Lo and behold, another job offer came through in March, and he took it. DS graduated in June, 2015, and we moved in July.
A few thoughts/clarifications on why we went the way we did:
First off, our son has Asperger's, is very introverted, and has a few learning disabilities. We briefly considered leaving him behind, but felt it would be too damaging. YMMD, but for our child, it just wasn't the right choice.
When DH was weekend commuting, he rented a room from a co-worker (I think he paid $50/week). That got him a bedroom and bathroom, 3 nights a week, plus the occasional meal. Due to the high cost of living, moving the family to this location wasn't going to happen.
Our younger children handled the move fine (they were starting 7th and 4th grades at the time). I wanted to move before the 7th grader had to choose her HS track, if that makes sense. We moved to a destination with multiple choices for HS kids. DS19 is living at home, and will for the foreseeable future. He's commuting to the local community college, studying at his pace. It's working for him. We also have a DD21--I'm sure she would tell you that she feels like a visitor in our home these days. Her heart isn't in the new state, which is okay. She graduated college this spring, and has zero interest in moving back home permanently.
Is there a chance of you AND your son staying with BIL? It might be a bit cramped, but I'm thinking you could be there with your son, and maybe all work together on household stuff, pitch in with the baby, and so forth.
I just keep thinking back to my neighbor's kid, and how the girl really felt like she was "ditched" by her family. I understand that circumstances are what they are--in that particular case, the family moved a lot for the dad's career, and I got the feeling he didn't give the slightest thought to how it affected his 5 kids. I'm sure that a sensitive, in-tune parent can make it work, I've just seen it not work so well.