Hi atlbuzz. I take it you're one of those people who REALLY LIKES coffee. My husband is one of those and I can't imagine him ever giving it up. So, to your question - No, of course you don't have to give up coffee. Some people do find that caffeine makes the RLS worse. And some people find that it doesn't make it worse. If you know that it makes the RLS worse, then you have a choice to make - do you just take more meds to cover the increased symptoms or do you cut the coffee, or drink less of it, or whatever.
I'm not a coffee drinker either. I do like tea occasionally, but chocolate is my favored source of methylxanthines (caffeine family). I try to limit it to early in the day when it can't get me too jazzed up to sleep, but there is no way I'm giving it up. I'll give it up when they pry it from my cold, dead fingers.
You say you're taking anticonvulsants - how well-controlled is your RLS with those? There are lots of options for treating RLS. In the "New to RLS" part of the message board, there is a sticky at the top with lots of information on how to treat RLS.
It's always good to look at things that could possibly worsen RLS, and then try to eliminate the ones you can. Many medications can worsen RLS, caffeine often does, as does alcohol, even things like too much sugar can bother some people, and one of the common offenders is ice cream.
It sounds like you've been through a lot of unpleasantness in your life. I'd say to take your comforts where you can get them, and if coffee is one of them, enjoy.