At one point, you and your teammate's pokemons register a very low HP (1).
At one point, your and your teammate's pokemons register a very low HP (2).
Which of the two sentences is correct?
Two Sample Utterances
At one point, you and your teammate's pokemons register a very low HP (1). [OKAY]
At one point, your and your teammate's pokemons register a very low HP (2). [NOT okay; much too awkward]
At one point, your teammate's Pokemon's and yours register a very low HP (2). BETTER
It's best to state the thing first and place the pronoun yours [his, hers, theirs, ours] after that. It is much clearer.
The second is correct. Consider removing some words, and see if it makes sense:
At one point, your pokemons register a very low HP.
At one point, your teammate's pokemons register a very low HP.
The first would have to be rewritten to be correct:
At one point, your teammate's and your pokemons register a very low HP.