When to tell my child and step child?

I have a 6 year old daughter who lives full time with my SO and I (but from my previous marriage). She is going to be ecstatic to be a big sister. My SO's 7 year old daughter only sees us in the summer because she lives in a different state. My so visits her every other week but it just isn't possible for us all to go. Unfortunately, she doesn't like me or my daughter. Her mom talks negatively about her dad's "new family" and tells her that we don't care about her (which couldn't be further from the truth). His daughter recently said that if her mom got pregnant, she would punch her in the stomach. I'm so worried about what her reaction will be, how to tell her, and when. We want to wait to tell her until she's with us in the summer and we have three whole months to be with her before her mom gets to chime in. The problem is that we want to invite her to my daughter's birthday party in May but I'll be showing by then. If she finds out I'm pregnant and then goes back to her mom, her mom will make sure that she hates this baby before she comes back in the summer. But I also don't want to not include her for the party. Any advice?