[Solved] Private Nursery

Backstory: my 2 year daughter lives in Scotland with her mother who is in university, I live in England studying at university (final year) and we are separated. I give her mother £40 weekly even though I no longer work part time (gave up work in November to focus on my final year). Legally I don't have to give her anything being a student but I would never do that and have kept up the £40 weekly. (Which I discovered recently is the amount someone on a £18,000ish salary would pay!)

My daughters mother (let's call her C) wants her to go to this private nursery and eventually the school. I don't like the idea but I'm ok with her going to the nursery as it doesn't cost much more than normal nursery (something like £2.50 a day, or so I’ve been told).

I visited 2 weeks ago and C had written down the costs etc and then the monthly amount at £843.

She had £843 - the funding/grants she gets from being a single parent, then she had me and her mother giving her £40 a month each. I worked out a day or two ago that after the funding taken off of it would leave £60 so would mean £30 off me and her mother not £40.

Anyway so she called me earlier telling me that she’s going to pay it every term instead of monthly as theres a 2.something% discount, and she said she needs £133 from me every 3 months which works out as £44.33 a month. I’m sure she said her mother was going to give her £120 every 3 months, but I can’t remember.

I said I can’t say for definite as although I’m about to graduate I can’t say for certain when/if I’m going to get a proper job, then she started to ask if my parents could ‘sub’ me for it until I do. I just said I’ll have to think about it.

I was getting confused with the numbers she was throwing at me so I said to her look lets go through it monthly like I’ve got it written in front of me as she wrote it. So I explained to her that after her funding it would leave £60 a month to be paid not £80, thats when she said her mother wasn’t going to give her £40 like she had written down. And then she was like look don’t worry about none of that I’m paying it termly for the discount.

So I said ok how are you now asking me for more money than was written monthly when there’ll be a discount that wasn’t on the monthly? She said she hadn’t worked it out with the discount yet. But even regardless of the discount, it's still more.

Then I asked her to send me it all written down so I could look over it. This started an argument. She was saying things like...
“No you don’t need to see how its worked out”
“Why do you need to worry about the other money, you don’t.”
“All you need to know is that I need £133 from you every 3 months and it’s not exactly much is it”

and things like that. I argued back, I told her that I am well within my right to ask how our daughters childcare is being paid for (am I mistaken?). She piped up saying she’s not lying to me or asking me for more than she needs. I said I’m not accusing you of that but I still want to see it written down so I can look over it better.

I pointed out that she didn’t have a problem showing it me the last time she calculated it or me taking a photo of it for reference purposes, so there shouldn’t be a problem now, especially as she’s asking me for more money. She said there shouldn’t be a problem and I shouldn’t be asking as I already have this copy, regardless of them now being incorrect.

She also tried to threaten me (at least that's how it came across) by saying that if she signs it but then if for some reason our daughter can't go there for example if we can't pay then it doesn't matter because she's signed so we would still have to pay and my name would be on there too?! Seems she doesn't realise she can't sign something in my name...

I didn’t give in and eventually as we ended the call she said she would send them to me when she got off the phone.
Half an hour later and I got a text off her where she said "I don't think I should send you how our daughters childcare is being paid for" using the excuse that her funding is going to pay for most of it and she isn't asking me for much.

Am I right in thinking that if I went to a lawyer they would tell me the opposite? In my mind this is either a power play (most likely) or she’s asking me for more than she needs.

And the thing that really gets me is that she doesn’t understand that the money I give her is all one payment, for everything. There’s no separate money for childcare. If we did it through the government it would be one amount set from my salary.

I don't want to be a [censored] and stop my daughter from going to this nursery, as she really liked it there. But without any guaranteed income right now and without knowing what starting salary I'll get when I do get a job I can't fathom how C can expect me to give her £51 every week...

Sorry… longer than I intended. Any advice would be greatly appreciated.