It's pretty typical, especially with difficulty bonuses. If the problem is your allies taking your supply, try the border avoidance tool mod. AI USSR is a bit weaker on purpose now though you can change that in the options. It shouldn't normally lose Moscow that fast but a buffed Axis is different of course.

There's a lot you have to do right when doing these invasions. Make sure you take advantage of every game mechanic to maximize bonuses for your armor. Move fast with your armor after landing before the AI can organize a defense. Land in several spots which tends to confuse the AI a bit. Link up the landing zones and try to encircle the defenders at the same time until you get a permanent foothold. Etc.

Well, i haven't stack enough figters planes so i loose the air superioty too soon. So i guess it's over, I can't push or even fall back to try another landing.