[Solved] Young and confused

Hi,

I am a 19 year old father of one, me and my ex split up in January of this year after a 5 year relationship, I currently work full time and she is a university student, my daughter is a resident at her address, my story and my confusion stems from this. I currently have a private arrangement to pay my ex £120 a month towards my daughters daily living costs, however, I see my daughter more than my ex, I pay for my daughters food when she comes to me and for my daughters clothing, I see my daughter on average 4 days a week leaving her mother with 3, her mother who receives more money then me, lives rent free and council tax reduced, she buys the food in her house in bulk yet rarely eats there, given all her free time away from her daughter she spends large quantities of time with her mother or current partner, I cannot drive and have an agreement that she will drop my daughter off, this will soon be coming to an end and I will have to find other ways to transport my daughter, my question is this, am I legally obliged to be paying money to my ex partner that evidently does not go towards the financial and health wellbeing of my daughter, my ex is well of financially with a care a property and a holiday booked. I feel I have been presented the short end of the stick I am terrified that if I change this agreement even slightly that she will force me to see my daughter less, I come form a very 'hard' background, dysfunctional family and all that, I work hard, I have a 2 bed house, space and food for my daughter, however, it seems when I am looking at the internet that the fathers really are shitted on, I am not saying I will not pay for my daughter, I do regularly I act like a father it is the business of this £120 which was set up because neither of us particularly wanted to go through CSA what I am trying to establish is this, if I grow the [censored] and have things set in place and refuse to pay her, money that I do not feel is going towards the wellbeing of my child (as I am paying this money) what can she do about it? I am getting to the end of my tether I am trying to b a reasonable man, looking at expenses being dwindled [censored] I do not have a weekend to myself and my partner as my ex was more than happy to put my daughter in my company whilst she went off gallivanting about.
I never expected it to come to this, she despises the ground I walk on and I am an emotional wreck, this potential legal business is [censored]. I am not a bad father I try so very hard to give my daughter that which I did not have and when she looks in my eyes telling me that mommy is better WHEN THE [censored] PRACTICALLY ABANDONS HER ON MY DOORSTEP it really makes me question the point of me being a father, my daughter idolises her mother and see's daddy as the big bad wolf as he says no, but when your income only covers the bills this extra money which seems pathetically wasted on my ex seems stupid. honestly this is not an exaggeration the woman has no I repeat no money issues whatsoever the extra income is a vicegrip on my [censored] as a fee to see my child nothing more and Is et it up in desperation, no written documentation just a verbal agreement, on the other hand, my expenses are not covered 😆 😆 😆 at all, £605 rent £115 council tax, gas electric, internet, phone, debts its all the rage my side my income of £1400 p/m does not allow for lots over, more debit then credit. I must be rambling I have been adding parts into this for some time now and am slowly starting to lose the plot, hopefully it makes some sense to you. 😆
sorry about this but honestly if I don't get an answer soon (not being threatening) I feel I am going to make one.
this is the first time I have spoken about this so I apologise about the mix match.
on a side note my daughters 'expenses' are covered by my ex's child tax, housing allowance, student grants, loans Jesus the woman is getting £6400 every 3 months with no rent or council tax, the nurseries bills are also covered.