It sounds like your problem arises when you ski with "more advanced" friends who ski fast down blue runs with only a few stops along the way.
You mention that you make wider turns than they do, and I'm assuming this is to avoid going too fast for comfort. That's wise!
Your legs hurt in the evening and turn to jelly the next morning. You mention leg fatigue.
I'm assuming your quads (thighs) are burning at the end of a few hours and at the end of the day they are quivering with overuse and exhaustion.
It's dangerous to ski when your quads are quivering. Stop skiing before they get this tired; bad things happen at this point.
You are wondering if the width of your turns is causing your leg problem, and you want to know what exercises can help you be stronger so this won't happen.
If I've got this right, your problem is how you balance on your skis, not how wide your turns are. If you have your legs coming straight up out of your boots as
you ski (shins perpendicular to skis), and if you are in a crouching position, half-sitting, your quads (thighs) will get a massive workout. Do you know what a wall-sit is?
If you balance on your skis the way I just described, then you are doing this all day. Skiers don't need to do this, but sometimes they get into this habit.
If this is you, then you are in the "back seat," you are "sitting back" on your skis. It's very common. Doing wall sits all summer would help, but it's just a bandaid on the problem.
If you're skiing in the back seat, you might look something like this. Looks like wall-sits, and works the quads the same.
The fix is hard to learn to do but very worthwhile. You need to work on balancing on your skis as you are moving with this stance as your "home base."
The fist big difference is getting your knees over the toe pieces of your bindings. That means
you will need to tilt your skins forward as they come up out of the boot. Always. Always. Always!
And you will need to hover the rest of your upper body forward-ish as you turn right and left.
You can see this forward hovering in the picture above. No sitting! Stand up taller and hover forward.
Keep those shins tilted forward and your body hovering forward so at least half of your weight is in front
of that dotted line up there in the picture.
Your legs will be thankful, and your turns will be easier to do.