I taught children's Aikido for 3 years before I got pregnant with my first child. You can find dojos that will take kids on a more relaxed basis. Try Aikido, because on the whole it is non-competitive. There is a reason that makes a difference, and I think mainly that Aikido dojos are less likely to be focussed on belt advancement. (This could just be my personal experience in the Seattle area-- a very diverse area as far as that art is concerned. Some dojos were more relaxed than others.)
As far a going twice a week or more, you really do pick it up more than twice as fast. I've heard my girls' gymnastics coach comment on this as well. Because it happens in Aikido-- where arm and leg strength are less crucial-- I know that it is more than just the physical aspects of the arts. But you shouldn't feel pressured to do it this often. The other reason for commitments is that most dojos are for-profit and need to pay their teachers. You can't do that on drop-ins, I guarantee it. Then there is the prestige of a full class. People dropping by *will* notice class size. A dojo with fewer than 4 kids in a class will most likely be passed by for the dynamic dojo filled with kids. I know this because my dojo was the quiet one. Luckily we were non-profit. Even so, we barely skimmed by some years.
I didn't start studying Aikido until I was 27. That was my first martial art. 7 is a magical age to start martial arts. I saw it over and over again with my kids. This sharp, knowing focus would magically appear and they'd "get it". But you don't have to start now. Bide your time and keep looking, you won't regret it.