Well, Teutonic/Livonians Knights did tried to takeover the region OTL and managed to take Pskov three times (1212, 1218 and 1240 : you may recognize the background of
Alexander Nievsky for the last one).
A germanic victory at the Battle of Lake Peipus would be interesting, but Novgorod's victory had far less importance than russian historiography tried to imply : Teutonics Order managed to grab more territory after their defeat (western side of the lake and Iourev/Derpt).
If the battle if definitely a teutonic victory, we could see Pskov being integrated as all the eastern side of the Peipus Lake, admittedly, but Teutonic/Livonian presence was relativly weak in these regions : an equivalent of
Wesenberg is still possible.
Eventually, even by gaining dominance in the XIII century against Novgorod, I doubt they could have made a lasted domination in face of Russian states for long.
You would have, on the contrary, the emergence of a (small) germano-russian nobility comparable to germano-baltic one and possibly a russian Border more weastwards than OTL, even if the wars of reconquests are going to be bloody (it's guesstimated that some places lost up to 1/2 of their population).
I don't know if you can read french, but
this article is quite exhaustive on the historical relations between Pskov and germans.
That said, balance between Russians states would have been probably changed with a Novgorodian (is that the word?) defeat.