No you can't sue "the system" and there's nothing in the information you provided that suggests gender discrimination or abuse.
Your attorney is correct. If a party refuses to comply with a court order the proper step is to seek to have the court enforce the order, most likely through a motion seeking to hold the party in contempt.
If you don't bring the other side's non-compliance to the judge's attention, how will he know? If they other party is truly in contempt and the judge grants you motion you wil likely get your legal fees paid for. In addition, it could change the entire tenor of the litigaiton.
My advice is listen to your lawyer. You are engaged in an emotional litigation and all of the thoughts and grievances right now are not connecting.
You have many valid issues but you are going to have to get them into court and that requires legal representation and paying an attorney. Failing that, you should spend some time in the law library and reading books on the topic of family law. To answer your question - I don't see any grounds here to sue the lawyer of your ex.