How to handle new girlfriend around my kids

Started seeing someone about 4 months ago and it's getting more serious. My ex found out and immediately said I can't have her around the kids and that she'll take me back to court if I do. But I'm not talking about moving her in or anything crazy, just like picking them up for an afternoon sometimes. I asked a lawyer friend and he said the court cares more about what's in the kids best interest than the ex's preferences. Any dads been through this? I'm trying to take it slow but I don't want to sneak around either.