I think you’d be better off posting this in the Living Overseas section, tbh. You’ll get advice from those of us who’ve made similar moves.
IMHO, you need to do it cold turkey. All in one go. Leaving them behind is just prolonging the agony, and risks you being stuck in one country and them refusing to come out.
It’s doable, but very much depends on where you are moving to. For example, are school fees being paid by the firm? Will the children be going to an international school (easiest but most expensive option unless they speak the local language). Are you being offered a relocation package? A consultant to help with visas etc?
We moved away from UK when DS was 10, in the middle of Y5. At 12, I’m guessing your oldest is Y7 or maybe 8? Hard time to move, unless it’s somewhere like an international school, where all the kids are used to people leaving and arriving and seem to just make friends quickly.
Things like healthcare you can sort out before (presumably there’s healthcare included?). Again depending on where you’re moving to, online banking will see you through until you have a local bank account sorted. I opened an account via video with Starling and relied on contactless payments for the first few months until cards and things arrived, before sorting a local bank account. Revolut is also your friend here.
In our case, my DH moved over the year before, but stayed in temporary accommodation. I took DS over for weekends and half term, to visit schools and areas/apartments. It’s essential to get schools sorted first, which then dictates where you’ll be living, and much better for your children to have visited the school with you first, so they’re invested. We teed up the school, chose our apartment, and then decided on a move date. We were fortunate that DH firm paid for international movers, but obviously all the packing was down to me. We kept our UK base, though, so not a full move.