We moved to be near family. We had some money saved but we moved in with family and job searched just as you plan. We, too, put all our stuff in storage. We moved the end of May and were able to get our own place by the end of October. Once my husband got a job we began the search for a small home where we could easily keep bills down. It was totally worth it. Yes, we struggled for a couple of years but having family nearby was a support system we hadn't had before. And it was huge!
1)Can your husband speak to his ex about concerns? She must know by now that he wants to keep up the payments and be close to his kids. If you think she can appreciate that (plus I'm sure you will be a help to her) maybe she will take the pressure off a tad if he promises to make it up to her IF he has to back off for a couple of months.
2)Cut every possible bill you can. Don't eat out and find yourself something part-time or something you can do from home...... anything..... temp jobs, I do a home business (email me if you want info), a couple of hours at the local Hallmark, babysitting, driving a neighbors child to or from school, walking dogs, housesitting. I don't know where Logwood is, but there are a lot of elderly people where my MIL lives. Many would pay someone just to take them to the grocery store once a week.
I follow the old saying: Nothing ventured, Nothing gained.