If you are constantly having to fall back on your strong hand, and use it as a crutch that is not good. You need to be able to develop your weak hand so that it is as good as your dominant hand. This means that you have to spend time doing basketball drills that are going to work on your handles, and give you confidence in your dribbling abilities.
Two basketball dribbling drills are a great way to balance yourself out as player. They will help give you confidence to dribble the basketball with either hand because you don't have the ability to switch the basketball over to your strong hand. You don't want to be predictable as a ball handler and if you can only go one direction while dribbling, you become very predictable.
Drill Name: Progression Crossover 2 Basketball Dribbling Drill
Drill Goal: Work on both hands at the same time and work on your crossover move
Equipment Needed: 2 basketballs
Tips: Make sure you keep your back straight and eyes up. Stay low on the dribble.
Directions: Take 1-3 stationary dribbles with each hand (as you get more advanced, limit your dribbles), and then cross both basketballs over in front of you. Use another stationary dribble(s) and do the same crossover move. Alternate which hand dribbles the basketball in front each time (it will end up the same basketball being in front each time). Continue this pattern for the desired amount of time, usually 30-60 seconds.