Yikes! Don't let the rats live in the enclosure with her! They can decide to start eating the snake.
She might be less "quirky" if she felt a little more secure. BPs are shy animals and those half log hides don't feel hidden enough for them. Also it helps to have 2 hides, one in the warm side and one in the cool side, so the snake doesn't have to choose between feeling secure or thermoregulating.
I'm not sure what you mean by exterior thermometer. If you mean the kind that sticks on to the tank, that only measures the temperature on the glass (the outside of the glass), not on the substrate where the snake is. If you mean an indoor/outdoor thermometer with a probe, that is great.
Unless you have some sort of t-stat or rheostat (dimmer) on those UTHs and lamp, I bet the temps in the tank are too high.