On the one hand, I would say that when it comes to your kids, you shouldn't bend. That is a time to hold to a boundary.
On the other hand... how old are they? Have they never been to sleep-away camp? Would it really be such a big deal for them to be away from you both for a couple of days, or would it simply be part of the inevitable march towards greater independence that all children are on?
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.