Ok, having lost my dad suddenly at a similar age to your eldest, and my mum did something similar moving us to the other end of the country, here’s my 2p worth.
i lost my dad. Then I lost my house, my school, my hobbies, my neighbours, my friends. That was a shit ton of loss in a very short time span. Everything I’d ever known and my security.
so just bear that in mind when you make your decisions.
if you travel, do it now before they settle. It may not be a bad idea as a new school, house etc will all feel very alien to them, it might be good to get some distance between their dad’s death and their new lives. So it doesn’t feel like a complete before and after. They need some transition time.
I never express myself well and I never seem to be able to get across the enormity of my loss as a 10 year old. There was such an attitude of kids adapt, they’ll be fine. While I felt like I’d had my life taken and plonked into someone else’s life. I never did adapt.
lastly- you are their world now and it’s a big deal. Be careful they don’t try and make themselves responsible for your happiness. I suppressed all my own needs and wants to keep my mum happy. If she even suggested that doing x would be better than y, i’d do X, no matter how desperately I wanted to do y. Listen to them.
sorry for your loss. It’s shit.