Thank you for requesting me. Please note: This is general information for educational purposes only and is not legal advice. No specific course of action is proposed herein, and no attorney-client relationship or privilege is formed by speaking to an expert on this site. By continuing, you confirm that you understand and agree to these terms.
What kind of things? Like arguments, alleged alcohol use, criminal activity, etc? If so, then yes. The other party can try to use anything and everything to argue that what you are asking is not in the best interest of the child
It does not mean that the Court will take it into consideration. Or, the Judge can even interrupt them and tell them that unless they have a point with the testimony they are giving, they need to focus on something relevant. Also, someone in your situation can object to evidence (testimony, etc) which is not relevant.
So the short answer is yes, they can. Rule of thumb is to be ready for anything.
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