(((Hugs))) she does sound OT, not nice at all for anyone.
When you say 11.45 in the car for a nap, how long will she nap?
In the first instance, to sort the OT, it might be worth considering allowing her to have longer naps (if she naps well?) with normsal BT to give her a chance to catch up. So in the 1st instance, maybe something like:
WU: 7am
Nap: 11.45 (for up to 3h)
BT:7pm
And then when the OT's dealt with reduce the nap if needs be depending on your LOs SN?
What do you think?