If it's any consolation, most people are fine when going back and forth and no problems arise. Even my husband visited me in the US multiple times during the process before getting approval. He was never asked anything other than "Where are you coming from?"
None of my friends from other countries or my husband's family members who have visited me have ever been asked anything other than maybe "how long are you visiting?" or "where are you going?"
Definitely take proof of ties if you have them of course, but generally MOST people aren't scrutinized too heavily especially those with an ESTA. Don't abuse it, and you likely won't lose it.
My husband always traveled with a folder while we were working on the immigration process where he would have documents to try to prove ties to go home (although he realistically didn't have anything strong at all lol) and he never once had to show anything at the border.
Congratulations on the baby!