In Florida, Can a custody lawsuit be dismissed before a hearing?

I have to answer this week to a custody suit my ex filed to have custody of our almost 18 yr old and her infant. I don't mind her living with him since that's what she wants after being dangled with she can have his apt while he moves into his new house.  I asked him to drop suit and I will modify parenting plan to state no one pays child support when she reaches 18 since she will be self-sufficient money-wise.  He said no.  Now we have to go to mediation at $120 an hr with cost being shared between us.  This is ridiculous.  Right now I'm dealing with child neglect case between teen and Dept of Children and family Services.  Her dad only wanted her after he learned of her settlement.  I typed an answer to lawsuit and will mail on Weds.  I have so much evidence but only answered that I disagree with some of what he is claiming.  Can this be dismissed before going before the judge or while in front of the judge?