You could request a mediation and trial date at a case management conference, but if the mediation date gets postponed for some reason, then your trial date may also be postponed. In my view, it would be preferable to complete mediation, and then request a trial date. But, that's between you and your lawyer. If you're represented and so is the other party, then you can tell your attorney in writing that you do not want to protract this matter, and that you are instructing the attorney to obtain a trial date at the soonest possible date, regardless of whether or not discovery is completed.
The attorney will resist your instruction, because:
(1) Attorneys don't like to try family law
cases -- it's expensive and time consuming, and the attorney has probably not mentioned to you how much more in advance fees you will have to pay, if the matter goes to trial. Moreover, believe it or not, unless a case settles, most family law attorneys are discharged by their clients before trial, because the client gets mad and blames the attorney for the delay and expenses. It's rare that a family law attorney who starts a case is the same attorney who completes the case; (2) It's malpractice to fail to adequately complete discovery, and it always takes at least 6 months to get it done. So, trying to push the case along, puts the attorney's license and practice in jeopardy -- which means that the attorney will either ignore your demands or offer to resign from the case if you persist in pushing the timeline.
I'm not saying that you can't have a trial at the soonest possible date. I'm merely saying that what you may believe that date should be, probably is too soon. So, I'm recommending that you write to your attorney, explain your concerns, and try to get some sort of rational timeline from the lawyer, so that you're not driving yourself nuts over the issue.
PS. In case you haven't noticed, I've done quite a bit of family law, and I can generally tell a client what he or she is thinking before the client tells me. I hope you take no offense.
so you have to make it clear that this is a requirement of the representation.