As someone who travels for 3 days every-other-month... don't do this if your husband isn't 100% supportive. My husband actually loves the time alone with the kids, but if he didn't I would not have taken this job.
You have posted about your husband's lack of motivation many times and now it is impacting your professional life, not just his own. He doesn't want to take care of the kids, he doesn't want to increase his earning potential, he doesn't want... he doesn't want... what do you want?
As I said at the start, this is a family decision in a sense because travel is tough. My husband turned down a recent offer because of the travel- we can't both be "travelers" and candidly I make more money and have better job security, so my job trumped his. We discussed it, though, in detail before making that decision.
If he's not going to be the primary caregiver while you are gone and is going to make you feel guilty for traveling, then don't do it. My husband mentioned ONE time that it must be nice to get to stay in a hotel and get a few days of quiet. My response? "Don't ever say that again- it's not "fun" while I'm away. I'm working and going back to a quiet hotel room to do more work and reading while you get to have cuddles and alone time with our kids." Hasn't come up again.