Just try to keep it fun for them. I started her when she was about six teaching her instinct shooting with a BB gun that has the sights removed. After a couple of years of this I moved her up to a 22. They learn pretty darn quick when young like that and she has always enjoyed doing it, now it's just second nature for her. As for the both eyes open, I've always been heavy into instinct shooting, that's where I started and I just feel anything you can see with one eye, you can see twice as good with two. Also, if you ever get into long range shooting, 1,000 or more yards, it's nice to be able to have the spotter scope where you can look through it while looking through your rifle scope. You can make your shot and then see the vapor trail through the spotter scope to see where you hit. I learned that way, I much less problems with eye strain when doing a lot of shooting and I'm just on of those that feel it's the only way to learn. I also believe the right way to cast a reel is, cast with one hand, wind with the other, not changing hands to wind.
We generally spend on day a week at the range. When we go I take all four of her guns and she usually starts off with either her pistol or 22 rifle shooting one of the metal flip targets. We have a lot of little comptitions with different guns, about the only thing I can honestly smoke her in now is shooting the tightest groups on paper and long range shooting. So far I'm still limiting her to 500yds because she has a lot of misses beyound that (shooting 6" square steel plates hanging from stands) but everything else she can hold her own against me. We may each stand 10 shotgun hulls on the ground at about 25 yards and shooting open sights free hand with one of the 22's or see who can shoot the most in thirty seconds or she who can flip the most disc on the flip targets. Then we may put a flip target at 200yds and again with a 22, see who can flip the most, the quickest in one load of a Remington 52 semi (it has a 4x scope in it). I usually throw some clay targets for her and let her shoot them with her 22 also, so she just has fun. The thing is, now she's starting to beat her papa at some of these games so she gets to come home with bragging rights. I also take her four wheeler so she can ride down to the 400 and 500yds targets to look at them. The range we go to is about 20 miles from the house and I let her drive to and from (all county roads) so I let her drive to and from it, which also makes her want to go. One good thing about being a little *******, country girl, she been driving since she was 10. That's with her in the drivers seat and me in the passengers.
We do a lot of stuff that's fun for her, around the boring stuff of practicing shooting small groups in the center of paper targets off sand bags at different ranges while having to learn how to make wind elevation adjustments. Elevations are easy because I have those on her scope for different ranges out to 500yds.
Then I make her shoot some rounds through the 243 T3 Lite, off the bi-pod or some other types of rest that would be more typical of hunting shots. She does not like shooting it because of the recoil but she wants to deer hunt this year and that's what she's going to be hunting with so she knows she's gotta do it.
The boring stuff and 243 is just worked in between so we always finish up with at least and hour of some of her fun stuff she likes to do. Most of the time I'm the one having to make her pack up to go home. Even on the way back from the driving range or her golf lessons during the week (she's also plays golf) we stop at a small pit near the house that's about 100yds long and 30yds wide and shoot her 22's for a 1/2 hour or so.
I've found what ever you do with kids, if you give them good equipment, treat them more as very young adults and not so much as little kids, you will be amazed at what they can do. She's also a pretty good bass fisher and can throw a Shimano Curado Bait caster as good as most.