I opened this post thinking you were going to be completely reasonable in your request - your child your rules so to speak. However, with every update you have given, I’ve never seen someone as entitled or unreasonable as you. By the update where you said your dad pays for your car I started to think that this post cannot be real, because no-one is this entitled surely?
I am going to reply assuming you are genuine though. GET YOUR SHIT TOGETHER OP.
Sort yourself out now for the sake of your daughter. Step up, and fucking parent her for gods sake. What is wrong with you? If you work 8-8, use breakfast club before school and drop her off before work. After school use after school clubs and then either a childminder or if your parents agree, they pick up from after school club til you get home. When you get back, you pick your daughter up straight away and take her home. If the school can’t accommodate changing days each week, pay for breakfast club every day, or ask your work for set days.
No more overnights at your parents. Full stop. Your daughter needs you and needs the stability of knowing she will be in her own bed every night.
Aak your local council for access to their “Early Help” team. They can be brilliant at helping you out. The school may be able to help with this.
You sound angry and beyond strict - almost abusive. I’m presuming you are taking your frustrations out on your daughter, and maybe once you don’t have to deal with your parents anymore, you won’t be so angry. But look at parenting courses and find better ways to manage your child’s behaviour that doesn’t involve trapping her in a room.
Stop taking your parents money. Are you not embarrassed over this? Not only are you not paying them for the huge amounts of childcare they are doing (just because they are family, doesn’t mean you don’t have to pay them - it’s different if it’s maybe one day a week that they offer to do, or just an hour after school each day, but you’re leaving your daughter virtually full time), but you’re actually taking money off them for your car. If you can’t afford the payments on your car without their support, you cannot afford that car. Get rid and buy a cheap runabout. Or just get rid and use public transport if that is an option.
If your ex is flakey, get to court and agree fixed visitation. I suspect what it actually is though is that you’ve left him to drop everything at short notice to fit with the days you are working that week - so he doesn’t get set days. That is not fair on him. Arrange for set days and you sort your childcare around that. I imagine it will be a lot simpler for him, and less likely to say he can’t, if he knows he has her every other weekend (and he takes her to gymnastics on his weekend) and say Monday/Tuesday after school/overnight whatever you agree. Then if he can’t collect etc HE arranges childcare.
Get into a routine. Establish boundaries for everyone. Let your parents just be grandparents, not her parents. You step up and do your part. You don’t necessarily need to change your job, but you do need to change your attitude to your daughter. She isn’t a part time responsibility. She’s your daughter and you need to be there for her all the time. If you have a day off, you do school runs, you cook family dinner to eat together, you take her out to the park to play after school, etc.
And if you can’t do all of that, ask your parents if they want to become her legal guardians, let them adopt her, and then stop confusing the poor girl. Although you should have made that decision when you fell pregnant, not when she is 6 years old.
And as someone else said, don’t ever have another child. Not unless you’re willing to put someone else first. Becoming a parent means your wants and dreams get pushed back to make your child your number one priority. It sounds to me like you want to live your life like a single, child-free person but have your daughter for aesthetics when it suits you.