It is likely that Catherine is no Tsarina in her own right there, only a Regent, since Pyotr was named the official successor, and with second surviving son from Catherine Peter would write the will in his favor (which is a plus compared to OTL, since it sorta butterflies the succession mess).
Now, Menshikov would be the de-facto regent over the boy (Catherine I was not much of a ruler, admit this) and would try to engage the boy to his daughter (
https://en.wikipedia.org/wiki/Maria_Menshikova ), like he planned OTL for Peter II.
OTL Peter II would likely be kept far away from politics unless the succession crisis emerges or the alcoholism of the parents still produces a child with mental retardation (though for Menshikov a Russian Carlos II is a boon), so there are troubles with male succession.
Really, out of late Peter/Catherine children (that is, born past 1710) only Natalya Petrovna (1718-1725) managed to be relatively healthy/OK. That's why chronic drunkards have bad fertility records.