Let's go back a little bit here. The idea, as I understood it, was that Putin hated Hillary and was friendly with Trump. Putin does not need specific control of Trump; likewise, Trump respected Putin as the charismatic authoritarian he so desperately wants to be, so his previous friendliness makes sense. Now that Putin is making Trump look weak, Trump has turned around. Of course, Trump still desires approval from daddy Putin, so he's moderating his response in hopes that things can be patched up.
Note that this whole hypothesis actually includes the possibility of a technically innocent Trump. If Putin and the Russian apparatus was working of their own volition to elect Trump, without collaboration, it's not exactly Trump's fault. I leave it to Muller and others to determine exactly how likely that is.
Frankly, the idea of compromat-ing Trump is a bit absurd. He has no shame, and his supporters literally cheered him on when he bragged about sexual assault and tax fraud. I believe that any material that would meaningfully weaken Trump would be so outlandish that it's not believable -- something on the order of weekly satanic cannibalism rituals at the Mar-a-Lago. And if it can't be believed, it's not effective compromat.