Do I have basis to file a slander/defamation of character lawsuit against a person if it has damaged my relationship with my child?
It's certainly possible. Slander is where someone says something that is harmful to someone's reputation and it is said with malice or negligence. Presuming you aren't a public figure, you would have to prove:
1)that the statement was received by another person (in this case, your child)
2)that the statement was false
3)that the statement was about you and tended to harm your reputation with the person who heard it
Please be aware that what is said has to come across as someone stating a fact. Someone saying their opinion won't get you there (ie, "My ex is a jerk" as opposed to "My ex is a pedophile").
Of course, you will want to have a local attorney thoroughly review the situation and discuss your options. You may find that using these statements as grounds for a change of custody would be more fruitful than a defamation action.
I hope this information was helpful!
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