Your atty should be able to file for temporary alimony and child support, until such time as you can finalize any D agreement, be it thru mediation or anything else.
As part of this motion, he should move that your husband has to pay all legal fees associated with the order.
Based upon your needs, your daughter's needs, and each of your incomes -- plus your husband's infidelity -- this should be a no-brainer. I know you like (and trust) your attorney, but I fail to see where he has served you well thru all of this, I really don't.
Your situation meets ALL of the criteria for immediate and temporary support!