The Roth rollover thing can work, but the 60 day time limit might be challenging.
If you both have Roths with enough, you could consider withdrawing from spouse1 IRA on day 1, withdrawing the same amount from spouse2 IRA on day 50ish and using the funds to repay the rollover from spouse1 IRA. Then repay the spouse2 IRA on day 100ish.
Since you own your own home, though, if I were in your shoes I'd probably be more likely to find some way to do the financing based on my home equity. They used to have something called a bridge loan for this kind of situation, I don't know if that product still exists. You could get a HELOC.
What I'd actually probably do, though, is sell house #1, park the proceeds in a savings account, then buy house #2. It involves moving twice (probably) but avoids financing hassle, so it's a tradeoff.