Potty training outside the house

My 2.5 year old daughter is in the process of being potty trained. She goes to daycare and wears a diaper at daycare but she does go on the potty at daycare. When she comes home we take off the diaper and she wears regular underwear with a vinyl cover. She hasn’t had any accidents in a couple of days and always tells me when she wants to go. I am just not sure how to transition this to outside the home? Because now every time we are in the car she tells me she wants to go on the potty. I have her diaper on her when we go out but I want to eliminate the diaper for outside trips, but then I feel like a nervous wreck worrying if we will make it to the nearest bathroom or not. I also do not like public bathrooms for her since they are icky and I don’t want her sitting on the seat? My friend carries her sons potty everywhere to deal with this issue but my daughter doesn’t have an actual potty just a potty seat that goes over the toilet. How do you guys manage?