I feel sorry for your DD2 dita poor wee thing, starting school is tough at the best of times. She will settle, and I think speaking to the TA will help, give it time.
As for your Dad, I think your mum's breakdown has contributed to this, and he probably IS stressed, and if your DD2 was playing up, was warned and still didn't temper it, then tbh what else could he have done? Carry on take her to his house and have her kick off there and stress everyone out including your mother?
No.
As tough a week as she is having, she needs to understand that we all get scared, upset and find new things differently, but screaming and shouting will not help anyone to help us.
I think your DH is right to leave the teas at the GP for a few weeks until DD2 is settled.
They get so very tired starting school, it exhausts them and it really plays havoc with their mood and behaviour even if they adore school and find it easy to go.
You need to spend some quiet time talking with DD2, explain to her that it's OK to feel a bit scared about new things, but tantrumming and being rude is never acceptable. Tell her that you know school is tiring, and that until she gets used to it, you'll both see your GP on the weekends only, and not in the week, as she needs her energy for school.
I don't blame your dad, not at all. It may have been harsh, but it won't do DD2 any harm at all to see that kicking off will never solve anything, and that she'll get more out of life and others by being well behaved and talking about things rather than screaming and shouting.