Hi there
I have been in your situation aswell, My DS has now been fully toilet trained for a good 3 months with only a nappy at night time and no pullup. This I think is just a phase she is going through and you just need to keep incouraging her to go to the potty. As for the toliet while out! I too did this and told him to just go in the pullup but i think it is the wrong thing to do, I just had to leave my groceries where they are and go out of the shop to find the toliet in the mall. Your groceries will be there when you get back. The more you do this the longer she will be able to hold on, and she will not need to go as often. This is so hard sometimes but im sure she will get there in the end.
The problem i have now is my DS LOVES going to the toliets while we are out, and keeps asking to go when he has only just been hahaha.
Theres always something ha ha ha.
good luck im sure she will be dry again soon