As far as the USA is concerned, this BBC article suggests that whilst the new rules are for vaccinated people, there may be some exemptions, including for children who aren't eligible for vaccination. But that sounds rather negative to me as eligibility is not the issue for your children and it seems to imply that children will require vaccines in most instances. But I haven't seen the official US advice and maybe the other exemptions might open up possibilities....
Covid: US opens up to fully vaccinated travellers - https://www.bbc.co.uk/news/world-us-canada-58628491
Edit:
More on exemptions here - doesn't sound positive
https://www.natlawreview.com/article...early-november
Limited exceptions will be provided for children; COVID-19 vaccine clinical trial participants AND humanitarian exceptions for those traveling for an important reason and who do not have access to timely vaccination BUT those granted an exception must agree to get vaccinated on arrival to the U.S.