It's a queer thing..but I've always thought that there was some sort of uneasiness between Snow and Julie, that was personal rather than Snow having to put up with his girlfriend/wife's best friend.
In Liliom, there is a character, a carpenter, who is in love with Julie, he has a very steady job, in contrast to Liliom (Billy), but she doesn't return his interest at all. I've often wondered if, in the creation of Carousel, Hammerstein had in mind to combine the roles of Wolf Beifeld - the equivalent of Enoch Snow - and the carpenter. Obviously, it's not spelt out in the script, but it adds a little frisson and I have seen it played that way.
Which, of course, is a long way from saying that Snow and Julie had a baby together, which is not there.