I'm sort of a whimp when it comes to coasters. It's one of the things I love about WDW - unnlike so many other parks, it SO much more than coasters!
BTMRR was always a ride I liked, but I was kind of iffy about Splash. Now that I'm older, I tolerate it better.
I finally went on Space Mountain five years ago. I really enjoy it! It doesn't have any huge drops. You can tell when the drops are about to happen, but at the same time, you aren't staring at the drops while you're in line. That helps me. I think if your kids are fine on Splash, they'll enjoy Space Mtn. I'm okay with Splash now, but it's still harder for me to go on Splash than Space Mtn. It can be hard on older people though, since you kind of get banged around in the seat. If you have back problems say, you might want to avoid it. On the other hand, we once saw a senior-aged couple on the ride that had special Space Mountain jackets - complete with LED lights. They were great!
Interestingly enough, the new Yeti ride LOOKS a lot worse than Space/Splash Mountain, but the ride is SOOOO smooth that it's only a bit more forceful than Space Mtn. It is more intense, but not by much. You also don't get banged around. The yeti might be a little scary to see, but you only see him for a second.