I'm right hand and eye dominate. Growing up, I had a few cousins that were left-handed and it was hard for them to learn how to tie shoes, etc from a right-handed person. So I would show them how to do it left-handed. Sounds simple but I learned something along the way that I used on my daughter. She's left-handed right eye dominate. Teaching her to play softball and basketball with both hands was not hard at all. All of these things have to do with muscle control, which starts with your mind. Many people underestimate just how much brain power is needed or used in a lot of activities. Setting up a ritual to follow, helps with their concentration. Take freethrows for example. The best freethrow shooters have a ritual and repeat it to a T, everytime. They have learned how to control their body movements and visualize the entire event in their minds before the shot. Samething with pro bowlers and other top athletes. We are tought to identify the target, place the sight(s) on the target, control beathing, safety off, squeeze trigger, etc. This is the samething here. Now move to the other hand and try it. You have to concentrate harder to control your movements, etc. Fundamentals are very important here. I've seen it many times in pre-game shooting. The kids were not making many shots(basketball). I'd tell them they had to make two offhanded shots in a row before they could shoot with their dominate hand. That's when you would see their brains start to kick in. It's easy to get in a rut with things you do repeatedly and lose your concentration. Challenge your brain and learn to do it both ways.
I've shot two deer left-handed. Knowing I could not get a right-handed shot off, I made extra sure my shots would be true. Strangely enough, the two deer I shot left-handed were the largest deer in the woods at that time. Without the left hand shot, they would not be mounted on my wall.
And if anyone is keeping score. My daughter is more accurate doing things right handed, shooting, batting, bowling, etc. She throws, writes and eat left-handed, can still bat lefty with more power than batting right. In basketball, you never know which way she will drive and shoot. But the most important thing, she has a very sharp mind. I let her figureout which way she will do it.