Do you have to serve the other party or just mail the court filed opposition to their Motion to Compel to the attorney?

Once a party is personally served with the Summons and Complaint and they're represented by counsel, you serve counsel with everything by mail. However, if counsel isn't situated close to where you're mailing papers from, be aware that C.C.P. section 1005 requires that opposition and reply papers have to be served by fax, personal delivery, express mail, "reasonably calculated to ensure delivery to the other party not later than the close of the next business business day" after the time the opposition or reply papers are filed.

Litigation is loaded with rules and deadlines, some of which, if not complied with, result in costly and irrevocable mistakes. You're best off hiring a litigator to do this.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.