Wow- I'm sorry you had such a bad time! But, like other people say, camping is an adventure!
Some things you might try next time-
1) a little more planning ahead can help a LOT. All National campsites have websites that you can check in advance to make sure the campsite you want is open and to reserve them ahead of time. You can get a lot of information on exactly what is available- toilets, showers, etc- and just have a much better idea of what you're getting into by doing research online beforehand.
2) Maybe the whole 'tent camping' thing was a little too much for you your first time out- nothing to worry about! My mom would never set FOOT in a tent, lol. But we often rented a little cabin- indoor plumbing and a stove and not too cold when the temperature dropped. There's nothing wrong with a little LESS 'roughing it'- most places will still have a fire circle outside, fishing and swimming docks, hiking trails nearby- just you have the comfort of being INSIDE if the weather turns on you! Some of my best childhood memories are of sitting inside our old fishing cabin, playing board games with my brother while my mom made a cake in the over while it rained outside.
3)Going alone is probably a good idea unless you are positive you and the other family are looking for the exact same experience. Also, although it can be nice to have more experienced campers to show you the ropes, personally, I prefer to make MY dumb mistakes in private without an audience, lol!
You just have to find your comfort level. Some people like to hike, some to fish, some to canoe, some cooks love the challenge of cooking over a fire and some people don't mind the tent and some don't need a tent at all! Just find YOUR family's comfort level and plan ahead! Don't be discouraged :)