Potential legal battle brewing with toxic family members involving my child - do I have enough to win?

So I may need to file legal action against an extended relative involving my child. I may need to get them legally barred from ever seeing my child again. Well, they think they can deem me unfit because of the past. When I was pregnant with my child, their dad was verbally abusing me and staged a setup to get me to say I wanted to kill myself. My child's dad had me on speaker phone where the problematic relative and another relative could hear it. I don't think it was recorded though.

This has been over a year ago and there is zero evidence that has ever shown me to have mental illness or be unstable or unfit. I have a good job, a place to live and am always the one buying and doing things for my child. I have proof via receipts that I'VE paid for 99.9% of the child's necessities (food, clothes, etc). I also could get proof from the child's doctor that shows I am always at appointments alone and the other parent has came to maybe two basic ones and maybe a couple specialist visits. I have proof via the child's pediatrician that I'M the guardian. I am labeled as the guardian and the other parent is listed as the primary emergency contact.

So, would this stand a chance in court? Could that seem me unfit? Even the responding officers at the time were not amused and totally dismissed the allegations and apologized for disrupting my evening.

I do not have video evidence of the verbal attacks, but I did document it and could take a lie detector to prove it. Could me yelling back at the attacker in front my son seem me unfit? I was defending us both. They were attacking me verbally and also making comments about my child and I let them know what I thought.

I also have documentation about their other behaviors involving my child that was inappropriate (trying to take control) and I have documentation of toxic behavior with them involving others that shows they are an aggressive person and a witness to back me up on that.

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I have a CRAP load of proof that shows where I have bought a ton of stuff myself. I have proof of where I pay for all medical care, provide insurance cover and as I said I can get proof from my child's healthcare providers that show I am the parent always there for appointments. And I can prove through documentation (no video) and witness accounts that this family member is highly aggressive and toxic.
Potential legal battle brewing with toxic family members involving my child - do I have enough to win?
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