Potty Training Part 2

Ok so I started potty training this week since I have some time on my hands. I have the potty in the living room and my daughter is bare bottom. She goes to the potty just fine. I have ordered some undies for her but got pullups tonight just to see. Well, I know they're like diapers and of course when I put them on her she peed in them. I know I probably need to see how she does in undies, but looking for some advice or suggestions. Obviously we arent going out anywhere but when we do I just dont know what to do. I dont want her to feel comfortable in a pullup and just pee but I also dont want her peeing in underwear and us having an accident in the carseat because that's a whole other mess. TIA! Potty training is not for the weak lol