What are my options under Florida law if I can't show up in person on my divorce court date?

What does your attorney say? You can ask the court for a postponement.

You would need to take care of the situation before the court date comes. If you have an attorney he/she should be able to take care of it, otherwise you could file for a continuence and have a good reason as to why you cannot attend the set court date. If you just don't show up, there are a few things that can happen... you need to take care of it sooner rather than later.