Transiton to underwear? Help!

My daughter Audrey is 22 months old. She successfully uses the potty if her lower half is naked. Obviously this presents a problem in public. She'll pee in regular underwear or in pull-ups, makes no difference if we're home or out. If she's got something on her bum, that's where she's going. What am I supposed to do????? I ask her countless times to tell me before she needs to go (works fine when she's naked). I don't want to put her back in diapers given the fact that she does use the potty when she's half naked, because that seems like backtracking, but I feel trapped because she'll pee in whatever I put her in. I have a family barbecue I'm supposed to go to this weekend, and I don't know what to do! She thinks a pull-up is a glorified diaper and okay to pee in, but if I put her in regular underwear (which she loves), she'll go in those too! Any advice? Should I just give up?