You can't project 20 years forward as if nothing is going to change.
George becomes Tsar, there would not be any doubt about that. His uncles would be the main power in the country anyway, and little would change.
Say George dies when he did in OTL, and Michael accedes. He's already seen his uncles run the country under George, and will have been involved as heir presumptive. Its likely he is able to assert his independence of action that much sooner, and as supreme authority he is able to contract a marriage of his own wishes, without as in OTL having his elder brother veto it.
Now its possible he won't meet Beatrice in the same way he did OTL, though he is related to her through the Edinburgh line so its probable he will. She's his cousin but this was no problem for most of European royalty, and he won't be blocking himself.
The question might be with regard to international relations - but here, you find that butterflies are playing havoc and what we need is a timeline and not a bash-it-out discussion!
Best Regards
Grey Wolf