If we lost a custody battle and have proof of perjury, should we counter sue?

You should appeal the court decision, and wait 2-3 months to petition the court for modification of custody. Please contact an attorney to go over the possible options. I don't feel that going after perjury will help you in a competent manner. However following the first sentence above may become beneficial for you. Above answer and comments to questions are for general purposes only and does not constitute legal advice or establishes an attorney-client relationship without a signed retainer. Please reach out to an attorney you are comfortable with working and discussing your case in more details.