Please don't shoot me down for this .. but zzz if school are saying she's settled when she's there and the upset is around the mornings .. have you simply tried not rising to it.
My youngest isn't as young as yours but he is a real stick in the mud - knows what he likes and likes what he knows. Initially he was very excited about school but that soon changed once he realised there were expectations to be met and work to be done in school and he wouldn't be getting his 'mummy days' on Thursdays without his brothers to share me with etc.
We got complete school refusal, wailing from the moment his uniform went on, refusing to eat, making himself wretch.. you name it he did it.
However the moment the door shut and I left he would merrily get on with his day, they videoed him numerous times because if I'm honest - I didn't believe them.
In the end I realised I was feeding into his 'dramatics' he'd start crying so I'd cuddle him, dress him, adore on him, sit with him with his breakfast, practically spoon feed him his cereal, carry him into school, constantly fuss and love on him .. he wasn't having to do anything independently, share me with his brothers who were pretty much having to sort themselves. So I stopped.
I would just ignore the crying and the flailing around, praise his brothers in a very OTT manner for getting dressed so sensibly, for brushing their teeth so well, for making their beds so nicely, for eating all the breakfast and clearing their pots away. Every single time he did a single thing remotely independently or without a fuss I payed the praise on thick, he was so clever, big, grown up, impressive, smart, wonderful. I'd pass him items of clothing and demonstrate where it needed to go, then angle my body so I wasn't acknowledging him until he'd start and then turn to him and adore him with praise and congratulations.
I'd lift him from the car, pass him is bag and wonder into the yard talking to one of his class mates about their bag, or shoes or coat to which he'd want to talk about his of course and follow us in..
As far as leaving went I'd made an agreement with him one evening away from tears and tantrums that I would walk him in, hang his bag and coat and help him self register, I'd kiss and cuddle him then say bye and leave.
I stuck to it religiously and school were very on board.
It took about a week to see a complete 180. Now he just behaves like his brothers and life has found a normalcy I expected from him attending school.
I'd would maybe wait until this has cracked the refusal to extend her hours but I would say it needs to be done by the summer or she's in for a rough ride come next September when she legally has to be there full time x