AIBU to question nursery refusing drop off before a planned outing?

YANBU. That's really poor for paid childcare. You're right to question the ratio, sounds like someone's off sick and your child's difficulties have been used as a means of managing that. I'd be asking for a refund for the half day that they couldn't accommodate her and looking for a new nursery.
Eta- they may have poor practice in general and that could be leading to your DDs meltdowns.

This ratio thing doesn’t sound right. However at our nursery we’re supposed to drop off between 8am-9am, or for the afternoon session at 2pm, to not disturb their activities, if there is something similar at yours then it might explain why they are getting a bit tougher on constant past 9am drop offs.

I'd be withholding payment for that session, as they have cancelled it (effectively).
I'd also be questioning why your DD is having meltdowns. If this is out of the ordinary, then there is clearly something going on that is affecting her badly. She is trying to communicate that to you.
Have a read of there's no such thing as naughty by Kate Silverston - it really does help with understanding children's behaviour!

What’s the normal cutoff? Our nursery had drop off between 8-9am if you missed 9am they had the right to refuse if they were doing something else.

It sounds like you were actually due earlier and were going to be late, based on what you wrote in your OP.

that cant be right to refuse you at 9 when she is due at 9.30
but i would make a bigger effort to get there on the scheduled time

Maybe they did only send enough staff to the park and someone stayed back to prep for other activities? I know you said the nursery was empty, but they are hardly going to say 'Well Jenny is here doing XYZ' because maybe that wouldn't be within their guidelines to just have 1 staff member and 1 child? I don't know, just trying to think of what could be going on.

You've clearly been late a lot of times for them to have to call you TWICE about the outing! If I was running the nursery, it would piss me off with someone consistently being late. If you were late for work that many times, you'd like have a warning.

That’s bad. You don’t leave 30 minutes early than you said especially if you checked with people that day.

I reckon they were short staffed and needed to keep numbers down to maintain ratio while out but didn’t want to cancel her attending as they would need to either refund the cost or offer alternative hours another day so and wanted a way out of accepting her for the morning (are their ratio numbers for a trip out different to if they’re staying on site?)

It is unacceptable for them to tell you at 9am that they can't accommodate your daughter for her booked nursery session that day.

Were you late or not? You said you would be there by 9.10/15 which is not late for 9.30.

Should add, my DD2 used to kick off leaving for preschool but we knew she actually did love it there and we trusted the staff completely. They were always flexible and really accommodating with supporting us to get DD2 in each day. They also made sure all children were included on their trips out, even if it wasn’t their day to be in.

What time is she meant to be there? To be honest, your DD’s reaction and the way the staff have reacted to you, I’d be questioning if it’s the right place for your DD.

Wow. That’s bonkers surely?? I wouldn’t be happy with that at all!