To further expand on what soniam said, someone under 7 must ride in the same "vehicle" as an adult. That means a unit that is a single car in a train. So, for Space Mountain, there are two cars per train, each with 3 seats, 1 per row. You could sit with your kids in one car, but you would not be allowed to have the under 7 child ride in the front car, and you in the second car, even if you were in the seat directly behind the coupling and they were right in front of you.
On Barnstormer, each car in the train only has one row of seating (unusual), which is why it sometimes leads to issues for people with multiple kids under 7.
I don't have kids, but this particular safety rule fascinates me for some reason.
Also, if you can handle BTTMR, you can handle Space. It's a bit rougher, but not really any more intense.