I would also still put an urgent application into court as well - simultaneously. SS is right - you should get social services involved. However, being somewhat cynical of them they may well say there is no risk to the child and it was just an issue with the Mother and the school. Which wouldn't help your case. Whereas if you apply to court you could inform them the school will only release their report to the court or the Police and ask the court to obtain the report from the school. Having social services involved in the background is fine - but don't hang about waiting for them to conclude things. It's well known Mothers hoodwink social services - who are overloaded anyway. If the court's involved they might order social services to follow up further and do a section 7.
So I think you need a plan.
1) Contact the new school by letter, introducing yourself as child's Father, with parental responsibility. That there is a court order of x date for your daughter to spend time with you, which has not been followed, and you have not seen her for some time. But as a parent with PR you ask them to keep you updated and informed of your child's progress.
2) Complete a C100 form for an urgent application for your daughter to live with you due to welfare issues which are currently being investigated and explain that the Mother has not been following the previous order, and you haven't seen your daughter since x date. Explain that the last time you saw your daughter she rejected you and said she had a new Dad now and your ex said daughter refused to see you. That you thought your daughter was safe until now. Submit a C1A with it for psychological and emotional welfare issues for your daughter. That will need filling out carefully as you don't yet have any evidence to attach to it. (Other than perhaps some emails or texts from your ex refusing to let your daughter see you and saying she doesn't want to see you - that will help). But in both application forms you can say - the school had to exclude your child due to aggression from the Mother and will only release their report to the courts and ask the courts to request it. Ask for it to be urgent ex parte - with the reason being given that if the other party is informed it could increase risk for the child (there's a tick box for that).
3) Contact social services and make the report and say it's after information from the school who have contacted you, and you have serious concerns about your daughter's welfare and have been unable to see your daughter for a long time and have had no contact with the Mother for a long time (so they don't see it as an argument between parents). If they refuse to open a case, tell them that you believe she is at risk of emotional and physical harm and you understand the Mother became physical with the school and you are also putting an urgent application into the courts to investigate but as your daughter is at risk of harm you wish them to open a case.
All three simultaneously really! That's my advice. Having had to try and open a case with social services before, I know how difficult they can be - especially with a Dad - and how dismissive of things they can be. The first thing they might say is - can't be an issue or school would have contacted us. To that you say - it was serious enough for the school not to want to deal with the Mother any more and the school was a protection for your daughter and ask them to open a case. If they still refuse then say at least will they authorise a police welfare check.
Tell them you want the report to be anonymous. They will do that. They might say - she will know it;s you anyway. But that's ok. She will only guess it's you! It could be anyone - even the school who've made the report.
This isn't really about whether you get residency or not - but it's about letting the court know there are welfare issues with your daughter and trying to protect her. They will pick up on the alienation aspect straight away (which is why you don't mention alienation - you just report what was said and what happened and let them decide that). And now there is something else.
Get the ball rolling and the courts looking into it. There is an expression that if you give someone enough rope they may just hang themselves. Your ex managed to exclude you and has still got herself into trouble - so can't blame you. Your daughter is in the middle of all this.
It sounds vaguely familiar. I wish my son's school had done this. Instead they all just went to pieces as they were scared of losing their careers (ex was threatening them and making formal complaints left right and centre). The question to ask is - why would a parent fall out with school? Because the school raised an issue probably and was trying to look out for the child.