In years past, some left-handed children were forced to use their right hand until it became their dominate hand. Many of these children grew up to become ambidextrous. If this works for a complex task like writing, then one might think it should work in learning to kick and punch.
You should train to fight from both sides (rather than training to perform all techniques equally on both sides). To do this, you should train each side to be "movement-specific," meaning that each side is trained to perform actions that the other side does not normally perform. For example, for a right-hander, only the left hand should be trained for back fist attacks and only the right hand should be trained for reverse punches. This means a fighter must fight from one lead all the time, even if it is the same lead side as the strong, dominate side. As a fighter gain experience, the fighter may train to switch leads, however, the training should concentrate on the dominate lead.
Most people are right-handed so they fight from a left lead, so they find it difficult to fight a fighter who is using a right-lead. So for this reason, if you make the right-lead your dominate lead, you will have an advantage over most fighters. Since left-handed people are in the minority, they are used to fighting right-handed people who fight with a left-lead. Right-handed people are used to fighting other right-handed people who fight with a left-lead.