The only way you'd give your genital herpes to a child is if you had inappropriate genital to genital contact with your children. Genital herpes is a sexually transmitted disease, meaning you have to have contact with the genitals in order to get it - think mouth to genitals (hsv1 genitally) or genitals to genitals (usually hsv2 genitally).
I'm going to assume this isn't happening.
You won't spread herpes (or any STD) via a toilet, or hands.
Use your own towels, but that's good sense, too - you could have a yeast infection or a skin issue, and you have little ones.
You are not a walking biohazard. If you hear nothing else, hear that. By all means, use good hygiene - you have little ones. You are helping prevent colds and flus and the like. Use the hand sanitizer when you camp, because camping is dirty, but not because you are going to infect your children.
Just remember that you are not a walking biohazard, okay? <3