It really depends on when in 1711 Peter dies.
Has he already attacked the Ottomans?
Has he abolished the Duma yet?
Has Alexis married Princess Charlotte?
If it is before these events, I could see an alliance between Sweden and the Ottomans - King Charles XII had taken refuge there after the 1709 Battle of Poltava, and Russia still held the Black Sea ports, surely a sore point to the Ottomans. Alexis is as of yet untested as a leader in battle, why not try to take back the Black Sea? Charles XII only concluded peace with Russia in 1721, he's going to want to take back his lands as well. Perhaps St Petersburg gets captured or burnt to the ground? What happens to the Russian Baltic fleet then?
Alexis apparently wasn't all that keen on his bride, does the marriage even take place is Peter is dead? Or does he marry his long time mistress, Afrosinia?
Did he really hate his father as much as is reported? I don't think he would have any interest in continuing the reforms of his father.
I could see Alexis restoring the power of the Patriarch of Moscow and the boyars, retreating to a palace and leaving the running of the country to them. He at some point wanted to become a monk, maybe he takes that path and abdicates in favor of his half brother Peter.
The Boyars would love that, they get regain their rights and power, while molding the future Tsar. Maybe Alexis (or Peter) marries Russian nobility instead.
I think Russia is going to be screwed no matter what.