A motion in limine is a motion filed with the court to include/exclude certain evidence at/from trial. A motion to compel discovery is a motion filed with the court asking the court to compel the non-moving party to produce discovery (evidence).
Should you not have an attorney, I'd strongly suggest you contact a competent attorney in your area for legal representation, as these motions, should they be granted by the court, could drastically impact your chances at trial.
Disclaimer: This does not constitute legal advice. No attorney-client relationship has been formed through this answer.
A motion to compel discovery is filed only after all informal means to resolve a dispute over discovery (i.e., attempt to gain information about the case) have failed. Typically, in addition to attempting to force the other side to give up the information by direct court order, a request is also made for sanctions, usually attorney fees in preparation of the motion.
A motion in limine is filed to alert the judge about an anticipated evidence controversy in the trial, so the judge can do legal research in advance in order to render a thoughtful, insightful ruling when the time comes when an actual objection to the evidence is made during trial. A motion in limine is advisory only, and the party filing the motion must still actually object at trial, to preserve any issues for a possible appeal.
From your question, it sounds like you as the defendant are the one considering filing these motions. A motion to compel discovery would be moot if the discovery has already been produced. If it was produced untimely according to the rules (typically the Civil Rules allow for 28 days on most discovery requests), theoretically you could file a motion for sanctions under Civil Rule 37, but in reality you shouldn't do that if you can't say you were adversely affected in any way. I understand from your question that the late responses caused the trial to be continued, and if so, the other side will have to answer to the judge for that. And if the judge reluctantly grants a continuance due to the other side's failure to produce timely discovery, they may not get another continuance in the future.
I don't see how a motion in limine is relevant to a tardy response to a discovery request, but if you still feel you need to file a motion in limine after the answer to this question, you should contact an attorney.