Switch hitting rule

[Cougar]

I have a simple rules question. We faced a kid who is a switch hitter today and he was far better right handed than left. Because of this, twice after he had gotten two strikes on him batting left handed, he switched to the right side.

After the first time we questioned the umpire if this was legal and he said yes, but we could tell he wasn't really sure. Because this was a "friendly" pre-season scrimmage game we didn't push the issue.

I have since done a quick look through the MLB rule books but don't seem to find anything on this subject.

Can anyone direct me to the rule on whether or when a batter can switch sides during his at bat?

If you can do it after two strikes, we have a right handed kid who is so fast that we will have him bat left and bunt for a double unless he has two strikes and then move to the right side and hit away!!

Seriously, if anyone can direct me to the rule on this I would appreciate it so we can make sure we are teaching the kids the right thing.