If a lady is modestly dressed, is she allowed to swim in a swimming pool where there are other men swimming? What if she makes sure that there is a distance between them?

Shalom U'verachah, The Gemara (Succah) says that in the Beit Hamikdash they made a good tikkun when they separated the men and the women during the celebration of the Beit Hashoevah. The Gemara then goes on to explain that it is appropriate to spearate between men and women in all cases where there is levity. Based on this I would definitely suggest that men and women do not go to the swimming pool together even if they are not in a state of undress. Kol Tuv