Sounds like you are going through a lot right now not only with current t stuff, but also ex-t and mom... any one of those would be enough to throw me for a loop, forget putting them all together.
One thing to think about, since ex-t is going through chemo right now, maybe she's not all on her game at the moment. She may just be handling the very basics. It may take her much longer than usual to get things together. chemo is excruciatingly grueling... I'm surprised she is in at all, but kudos to her for trying...
I'm not sure I remember how it ended witth you and ex-t (if it was just the fact that the cancer would make her less reliable, or if you guys ended for other reasons), but I would hazard that seeing her car through the window during current sessions would be a bit destabilizing. Even if you ended on a positive note, I could imagine myself wondering how T ws doing, was she being effective, does she think of me, maybe even a bit bitter that I have to start all over again with a new T when she's right there... is there a way maybe T could draw the shades or something? It might make being more present in session a bit easier.
Also, if it's been at least a week, and you and new T really need to get moving on dealing with the SA stuff you wrote about, could you give ex-t another call? Maybe ask if she's had the time to find it, and convey to her your urgency in getting the info to new T if it's somethign really pressing.
Is there anyway to make lunch with your mother more bearable? Maybe take someone else along with you? or dominate the conversation with talk of the weather, the superbowl, global warming, anything to keep her from being too focused on being judgemental? It's also ok to tell her somethign came up, and you are no longer available for lunch at the moment. Maybe re-schedule for a later time when you feel a bit more stable? Even if she is getting older, you shouldn't have to subject yourself to being that uncomfortable when you are already spiraling. There's no hard and fast rule saying we owe anyone anything. They may make us feel like crap for putting ourselves first, but you have every right to do so.
Hang in there for the appointment with new T, try not to cancel. It sounds liek you can use all the support you can get at the moment. New T may turn out to be really good for that.

hang in there. And vent anytime.