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Here's an idea: Get a different job, or seek a different position. One that requires you to move or do a lot of traveling.
If you're clever, your work schedule might coincide nicely with those times when the kids are at home.
That's the only way I can imagine you being out of the house a great deal of the time without seriously damaging your relationship with your husband, your relationship (such as it is) with the kids, and your husband's relationship with his kids.