Should I(29M) give up custody of my daughter(8)?

While I was studying in university I met my ex(now 30F), we dated for 5 months, before she got pregnant. It was an accident.
After she found out she said she would keep the baby. Honestly I wasn't ready to be a father, but I made the mess and I was planning on being there. That was until she wanted for us to get married.
I thought it was too early for married, but was willing and ready to move in together. That wasn't good enough. After many fights she told me that unless I married her I wouldn't be seeing our daughter.
I thought it was a bluff, which turned out to be wrong. Any gifts I gave or help I offered was turned down. The first time I saw my daughter was in court when she was 6 months old, when I finally established paternity.
I was given limited visitation since I hadn't been a part of her life from the beginning. After that I didn't see her for 8 months, since every time I went to her parents home for my scheduled visit they weren't there.
I went throw court again and I was given more custody now 2 weekends a month and ex was given a warning. Thinks were going decent until she suddenly stopped bringing her over, she demanded that she does the drop-offs and that I shouldn't be going to her home, the judge agreed.
That was my 3rd time in court, afterwards my custody became a full week, but my daughter was already 4. Ex did it because she saw a post of me and my girlfriend at the time going to a restaurant.
Then she used covid as an excuse and because court were moving slower that usually I was able to see my daughter in January 2021 but at that point we were given 50/50 custody, and the judge warned her that if she kept my daughter from me one more time or if she continued to tell her how bad and evil I am she will be losing her custody.
Since then there haven't been any problems in regards of custody, but now came the new problem.
Daughter started school last year and she started gaining abnormal amounts of weight. I was honestly worried. We did tests and visited many doctors, but all of them told us she was fine medically, but she needs to loose the extra weight since it isn't good for her.
I talked with ex and we decided that we aren't going to put her on a diet, but we will stop letting her eat fast food, cook more healthy meal and mostly focus on getting her interested in some sort of sport.
Nothing was working and I was honestly thinking I was going crazy. She kept gaining weight and would give up on any sport after a week or two. She had been to fencing, folk dance, running, zumba, taekwondo and mountaineering.
One of the instructors informed me that my ex never brought our daughter in when it was her week. I got suspicious and called the rest of the instructors, and those that remembered us confirmed that ex never brought here there as well. At that point I asked my daughter what she ate at her mother's and after promising promising to keep it a secret she told me that she lives almost entirely on McDonald's and chips and junk food.
I saw red our daughter is currently 1,18m and is 48 kg. She has problems walking because it's too hard, is been bullied at school, mostly unintentionally, kids don't want to play with her because she ruins the games, but there has been name calling as well from older kids. Her doctor has been getting really worried and her mother was doing it on purpose.
I decided to talk with her parents, they spoil her but care about my daughter more. After begging them to listen to me, showing them proff that it was dangerous for her health for her to be this overweight, and them paying for a really expensive doctor to tell them the same thing the agreed to help me.
They threatened to cut off ex if she doesn't get her act together. That was last month.
We had to put daughter on a temporary diet, low on carbohydrates, since her blood sugar was high and we are hoping that it will naturally lower it without any medication needed. We will know in 2 more months.
She doesn't want to try out sports, but I tricked her into going on walks with me everyday.
The problem comes from last Saturday. Me were on a walk and she was celebrating her catch, when she asked me for an ice cream. There are a lot of stands in the park we use. After thinking about it, I decided to allow her 1 since she had been acting great all week and hadn't caused a fuss over her food. I said OK and was going to lead her to a stand when she said she wanted it from the supermarket. It was fine by me since it would be cheaper, but when we went there she immediately chose one of the 720g tubs.
I told her to get a cone or a popsicle, but she insisted. My brilliant idea then was to tell that it will spoil in the fridge since she can eat it all by herself and I wasn't hungry. She said she can and that she eats them all the time. I thought she was lying, but then she started crying not to tell Santa. All in all her mother followed the diet, but let her eat a whole tub of ice cream after every dinner and daughter wasn't supposed to tell we since I was going to tell Santa not to give her presents. She didn't eat ice cream that night, but I calmed her down and promised not to tell Santa. I didn't talk with ex about it on Sunday since I didn't see the point.
Monday I talked with my lawyer about my options. The man has been my lifesaver since the first case. He told me if I take this to court my best option is to petition for sole medical decision-making. But in the best of circumstances it will take at least 2 years since the only evidence I have is my daughter's words and there will be stages to the whole process, but knowing my ex he is certain that she will shot herself in the foot. But that is if the judge isn't conservative, if he is there is the chance that he'll say "a fat child is a healthy child" and it might be viewed as me trying to take more custody. In the worst case I can even lose some of my custody time. He says chances are 60/40.
If I talk to her parents they will probably cut her off, if daughter confirms it, but ex is making decent money and has an apartment in her name that her parents gifted her, so she won't be in need of money.
I've been thinking and I'm honestly dreading the future. I don't want to spend the next 10 years always in court, living paycheck to paycheck and even having to ask people for loans, I recently paid the last one of and if we are going to court I have to ask someone else, I don't take bank loans since it has a negative effect in court, you are viewed as less capable of providing a stable home. And even if all of this actually works there will be something else in the future. I'm always going to be the bad one and her mother will be the fun parent. I just want to give up, I don't want to see my daughter become sick and/or disabled because of her mother's vendetta. I'm tired. If I give up my parental rights maybe everything will come to an end.
TLDR Should l give up my parental rights, because I tired of fighting with my ex in court and because it might stop her from using my daughter in her vendetta?


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