In 1862, Czechoslovakia did not exist. It was created as a country after WW One. I don't have my map book with me, so cannot look it up. (However, I did use the Internet and located it, I think.) The historians are happier when people asking the questions word them historically accurate.
What you need to determine is if Domazlice was in Bohemia or Moravia, or possibly Silesia or even Slovakia. When you find it on the map, then look for a larger city nearby. This would point out which archives you need to use to do the searching.
I'm apologizing, because I sort of know the answer, but my mission is to help new researchers to learn to use the system, and if we do the work for you, you will not become a future expert.
Then, if you have anything in a family document, it is a good idea to scan it and attach a copy here. Of course, if this is oral tradition, that's what we have to work with.
So your first step would be to locate Domazlice on a map, and any larger cities nearby.
Mary in Omaha