Diapers can leak for a variety of different reasons.
The most common reason diapers leak on a baby or toddler is because the diaper is too small and not absorbent enough or the baby or toddler is just peeing too much and the diaper cannot handle the amount of urine that the kid is putting out.
If the diaper constantly leaks then you may need to go up a diaper size or get more absorbent diapers.
Sometimes you might need to cut a slit in the first disposable diaper and then put another diaper over the first one to double diaper the child.
That way they have a more absorbent diaper.
I've had to do that with my kids at night or on road trips when they would wet heavily.
I would recommend Luvs diapers as they are cheap diapers but also very absorbent.