In the big leagues, a left-handed reliever is sometimes brought into the game to neutralize a left-handed batter. Lefty hitters tend to do well against right-handed pitching. Think of great lefty hitters like Babe Ruth, Ted Williams and Ichiro.
In youth leagues, there usually aren't many left-handed hitters on the opposing team - maybe one or two. Sometimes they are good hitters, but a lot of times they aren't. Once in a while, there is a switch hitter on a team, but they tend to have a regular side they hit from during a game. Switching pitchers, or pitching arms, between batters at this level isn't necessary and can dissrupt the rythm of a young pitcher. So I suggest alternating right-handed and left-handed pitching by inning. Start with the weaker arm, then switch to the stronger arm the following inning.
During a game, my son would usually start out pitching left-handed , then pitched the next inning right-handed after warming up in the bullpen during his team's turn at bat. He was allowed 8 warmup pitches on the mound the first inning and only four warm-up pitches for his second inning on the mound. It did not matter if he was switching arms between innings.
Using this strategy gave him more experience pitching from each side, rather than only facing one or two lefty batters when he threw left-handed.
If he struggled with his control left-handed, then he could fetch the other glove from the duggout and finish the inning pitching right-handed (no warmups allowed). It was nice not having to be pulled from the game, and it made him a better pitcher.
Sometimes he had to come in as a relief pitcher with runners on base, so he would throw right-handed, get ground ball outs and finish the inning. He would continue to pitch the next inning right-handed and switch to throw left-handed his third inning (after warming up on the side). He normally had a low pitch count, and could have pitched five innings but was only allowed to throw up to three innings in the 11-12yo division.
After a season of switch pitching, he was able to throw more strikes per inning than a natural lefty on the team. Of course, this takes focus, dedication and practice - lots of practice - but it can be done by an older player.