Trouble with starting school and the ex

My ex and I have a 4 year old daughter who is starting school in a couple of weeks. My ex and I split up a few years ago and I have a new partner, ex is with the guy she was hanging around with before we split but irrelevant.

We only talk about daughter, we've been to court as ex was systematically trying to remove me from daughters life. I now have daughter two week nights and every other weekend Fri-Mon, half holidays, so lots of school pickups/drop offs.

So I spoke to the school last term and explained the situation, I've been fully involved in raising our daughter, as has my ex. The school were lovely, they said they can do home visits with both parents, it would be lovely to meet the teacher one on one with daughter so she can show off her flower garden etc. But..... the ex has kicked off BIG TIME. She's not silly enough to say why but she is doing everything to stop the visit. She also wants me to give her my info for her to fill out the school forms rather than me fill out the second set of forms the school gave me etc.
I know my ex better than she knows herself, I know deep down her "single mum" status is threatened and that she is very insecure. She manifests it with horrendous aggression and controlling behaviour.

Im worried that if I dont stand up for my daughters right to equal parents, my daughter will lose out.
Im worried my ex and I are going to make complete fools of ourselves before school has even started. Theres nothing worse than squabbling parents.
Im worried because if I back down and cancel the visit she WILL claim that it was me that chose it and paint me as not bothering, and it will embolden her to alienate me more.
But most of all, at my age, my daughter will be my only child and she is growing too fast and I dont want to miss a moment. I invited my ex to go uniform shopping this weekend [Ive asked several times before] but she has already done it. Within her right of course, but hurtful since I would always invite her before buying the uniform.

Anyway, I know ex will go to the school and try hard to get them to cancel my home visit, how an earth can I stand up for my daughter and myself without it turning into a cat fight with the poor school stuck in the middle?

Sorry about the war and peace but Im so stressed, any advice would be hugely appreciated.