I’d rank the ones you listed in roughly this order:

1. Munich (far and away the best major airport in Europe for transits, in my opinion)
2. Zurich
3. Vienna
4. Frankfurt
5. Brussels

In case AMS is an option, it would fall mid-pack,
maybe between Vienna and Frankfurt.

I would avoid LHR and CPH with young kids.

Unless you have some kind of unusual circumstance, like a canceled or severely delayed flight or you have a long layover and want to visit the city at your transit point, you shouldn’t have to pass through any kind of immigration or customs checks when transiting US-EU-Russia. (Caveat: It’s been many years since I last flew to Russia.)

Good luck and happy travels! Traveling with little ones isn’t easy, but it also isn’t as hard as you probably fear.