Dan--so sorry to hear that things are not as they should be. You are in a tough position, my friend, as the harsh reality is that you simply cannot control the behavior of another adult.
Is this other person's behavior childish? Absolutely. Is it inappropriate to do in front of children? Incredibly so. I hear you and I know this has to be really frustrating for you and I am so sorry that it is happening. I feel awful that I cannot offer more than sympathy and an ear.
My best advice is to talk to the kids as much as you can...tell them how much you love them, how much they mean to you. And you know, it doesn't always have to be somber and serious stuff like "You are the most important things in the world to me" (though that is great to say as well). But really, it is the little things. Get to know them for the people they are. Participate in their interests. Find out what goes on during the day..again the little things. Who did you eat lunch with today?
This is what we do in our family...all of us...adults and kids. And we have done this since the kids were really young. First and foremost, we have a sit down family dinner every night. Sure, sometimes there is soccer practice or PTA or other life stuff. This means that sometimes someone has to leave the table early or whatever. But family dinner time is a big deal. I know you can't have that nightly with your girls, but you can when they are with you. Kids find comfort and feel safe with routine.
Then, everyone gets a chance to talk. And everyone has to say 2 good things that happened to them that day and 2 not so great things that happened. This has been the most amazing relationship building tool that we have done. Again, for J and I as well as the kids. This way, we hear the things that we might not otherwise hear (that then come out in other ways). If a kid was mean to them on the bus...if someone hurt their feelings...if their team lost at dodgeball at recess. Little stuff, sure, but it is these little things that can be HUGE in the life of a kid. And when they have to tell the 2 not-great things, well...that is how we find out about that type of stuff. And it allows the whole family to be supportive of one another. Corny, maybe, but it really does work. And most importantly, I think, they KNOW that we are interested in their lives and what happens during their day. They KNOW that they are going to get a chance to be heard and that we will listen. (This is huge for kids...remember that they live in an adult world where the message that is always reinforced is that "Our adult lives are far more important than what yours...")
This was hardest, actually, for J to get into the habit of. But now he really likes it. He spends his commute thinking about his 2 good things and 2 bad things.
Anyway...I got off on a tangent, sorry

but my point was that you need to talk to them every day. Be involved in their daily lives in the ways that you can. Be consistent. Kids want and need consistency and stability and routine. Be that for them and they will know the reality of your love for them.