LL- You can still go throughh mediation and engage your own attorney. In fact, ultimately you must in most legal territories in order to sign off.
Alternatively, insist on a mediator that IS a family lawyer. Ask one that you find for a referral to someone you can engage as your own. They will be familiar with each others' styles and help you get a feel for the mediator.
I did this and it's a wonderful thing. Total costs will be about 15% of the fully litigious court route. And even with a lawyer in court there is no guarantee the judge will rule in your favor.