I generally charge $15 an hour (once a week). For younger kids (the youngest I'll teach is 6, I've found that younger kids than that really don't have enough control over themselves to be able to control a horse too...and they have a harder time focusing on the teacher and they tend to be more easily frustrated, in my experience) I suggest to their parent that we can try an hour long session the first time, but I advise them that a 45 minute session might be better since younger kids have a hard time focusing for a full hour. I've been charging $13 for 45 minutes.
I think that a small child who's never ridden is quite a bit different than one who's grown up around horses, like you did. You probably had a sort of innate sense about them since you probably watched other people (grown ups) ride quite a bit (and how the mechanics of put the reins like this and the horse does that, etc), but a child that's never been around a horse is probably going to have a lot more fear and concern, coupled with less understanding about how horses "work", about what the horse "might" do. So that might another issue for you to consider, do you have the patience to work with a kid that may very well just want to sit on the horse for 15 minutes and do nothing else for the first few lessons? Are you able to put any agenda/lesson plan you may want to have to the the side and just go off of what the kid is comfortable with?
Another thing I found to be super important with my littler kids was to have a tiny (I think the one I'm using is a 10 or 12 inch) saddle. I'm actually borrowing one from my camp right now and that's been so amazing. It became apparent to me after my first lesson or two that my 15 inch saddle was not going to cut it. It might have been different if I was teaching on level ground, but those poor kids were sliding all over and having the hardest time letting go of the saddle horn (especially since the stirrups couldn't get short enough for them).
Another thing I do is I keep them on the lunge line for the first bazillion sessions (until they can stop, start, and steer without too much thought). Especially for the scared ones, they seem to really gain confidence knowing that they are in control but that I'm also in control if they need me. I like to do all sorts of crazy stuff with them, like having them stand up in the saddle, put both their hands in the air, take their feet out of the stirrups and put them back in without help, etc. I think those silly things really help them become more confident that they are going to stay in the saddle, it helps them develop an independent seat, and it helps them not rely on their hands so much.
And with the 4 year old, I would tread very cautiously, actually, I don't think I would do it. But that's just becuase I know Lacey isn't THAT calm yet and the facilities I have access to aren't easy enough for a child that small. If I had a perfect horse and better facilities, I think I would still be cautious. I mean, one scare for a 4 year old could really turn them off horses for life. But, at the same time, if you have the ways to do it safely and make it fun, I think that would be really great! I mean, I wish I had started riding when I was 4! I had to wait until I was 8 to ride a horse for the first time and it was lame to have to wait that long.
Wow, novel much? Haha Hopefully some of that was helpful! Good luck! Giving lessons is so rewarding. I LOVE it. The key is staying positive and acting like nothing is a big deal, even if your horse almost ran over the kid (Lacey.................LOL!). Lessons are great, and the gifts you get from kids sometimes? Priceless. Today my favorite kid (6 years old) gave me a sheet of paper that had a few drawings, each drawing (that looked sort of like blobs) was labeled in order: "cat, rabbit, horse, elephant, dolphin". It was super great.