I am the same way as your daughter. Right handed, left eye dominant, can't close my left eye but can close my right. I grew up only shooting rifles and shotguns, no pistols, so my case might be a little different. When I was a kid I spent a lot of time shooting a 22 around the yard, right handed, with both eyes open. Back then my dad had thought you were supposed to close your left eye to shoot with your right, and since I couldn't close my left, he tried to teach me with an eye patch. I didn't like the eye patch and preferred to have both eyes open. I think that shooting a scoped rifle a lot helped my brain to learn to use my right eye. A shotgun was a little more difficult, sometimes my left eye would take over. I tried shooting a shotgun left handed some, but couldn't do it. Today, I'm 30 yrs old, if I do the eye dominance test, it points to my left eye every time. But if I point a shotgun, or pistol, right eye takes over. If I point the shotgun at something close, like indoors within about 15 ft, my left eye usually takes over and I'm looking down the side of the gun. But if I point at something farther away, my right eye is good. If I try to shoot a gun left handed, my right eye is dominant and it is hard for me to switch to the left eye.
I don't know if it would have been better to learn to shoot lefty as a kid or not. My left handed coordination has always been very bad, but maybe that's something you can improve with practice. But I have no problems shooting right handed with both eyes open, whether its with a rifle, shotgun, pistol, or a bow.