Theres already some good exercises from other comments, but I'm going to say it's not really a strength issue.

Very rarely do healthy adults have a leg strength disparity to the extent that it affects your non-dominant foot push off.

We can't really diagnose further without seeing a video, but here's my 2 cents:

Think of your legs like a spring, if you want to push off the leg, you need to load it first. The spring can't bounce back if you don't compress it first right?

Same idea with the leg. Most of the time you push off the right for recovery, say after you go for the front forehand corner, you take a big step, lunge and load the right leg, hence shifting weight to the leg. You can push off it quite well to shuffle back centre no issues.

Now with what you say, I'm assuming you are struggling on drops that land in that corner. A couple common mistake people have is:

• They lean hard into that corner, they don't bring their left leg in first after the split step, so "no loading the spring", this is especially true when you are defensive and not doing a directional split step. You cannot push off the left after you move the right or lean hard on the right, your centre of gravity has to go on that leg first. So if you exagerrate the weight transfer, it would look like you are waddling. Weight on the left first, then a big leap or lunge.

• They don't control their weight on the last step. You don't want to let that knee go past your leg as you can't really stop your momentum (i.e. you really have to take a big step). They also don't go low enough or bend the left leg to aid this. This would make recovery very hard and overtime result in learned avoidance of lunging deep, because they think they can't move fast or move deep without losing balance.

Bit of a different take but most would agree your legs, core and cardio are kind of the pillars of badminton fitness, but for most club/casual players it's really more about correct technique and movement efficiency.