Will my sister find out I backed into her car?

I'm not an oracle.

There are usually telltale signs of 2 cars having intimate contact. Like your mother's red car will leave red paint on your sister's white car and vice versa.

If your sister's car has a collision mark on it 22 inches above the ground, your mother's car will have a similar collision mark 22 inches above the ground.

Also, it seems that a corner of the car that you were driving, hit a corner of the parked car. So when those cars are parked near each other, somebody will notice.

Or maybe broken headlight pieces are laying on the ground and will be found, so it will be known WHERE the accident happened.

It comes down to this: How was it that you hit the car? Was it dark? You didn't look while backing up? How did this mistake happen? And what kind of person are you (your character) that you want to hide your mistake?

You need to fix your sister's car damage. With YOUR money. Not your sister making an insurance claim, that will raise her insurance rate. YOU fix it!

See, YOU are the reason why my auto Insurance is as high as it is, You and your F'n, "sneaking" ...ie..( stealing ) created property damage. To your own family members property. That "they"...( according to you ) " Have no Idea how this happened" .. So, what they will do is make a Insurance claim, You little F'n Idiot, And that will cause all of our Insurance to go up. You Little F'n democrat..

Own up to your mistake. Get the damage fixed and pay for it. Learn to not crash. You took your mom's keys, you said, and I guess you may not have asked for permission. It's too late to pretend to be innocent. Quit being a rogue.

How old are you? Do yiu have your drivers license?
You know what ya gotta do....you dont need a bunch of strangers to tell you.
It eill be hard, but DO THE RIGHT THING! Because it will be a million times worse if you dont.
Your mother might even secretly admire you for stepping up.

And your sister might be mad nut mot forever. Fix her headlight!
Good luck tp you.

Yeah your sister's insurance cost will go up if they pay for it, and that isn't fair to her, insurance is expensive. Pick a time to tell at least your sister, maybe she'll be willing to keep it between the two of you if you come clean with her. But you should fess up regardless. Find her in a good mood first. Or do something like make her dinner to butter her up. Oh yeah you might even be able to buy a new headlight from an auto parts store and fix it yourself. Or from a dealer. Shop around, maybe you can find the part from a used car.

Do the right thing. Let everyone involved know that you took the car and broke the headlight. This incident has many lessons to learn.

Not everyone pays much attention to their car's body, barring serious damage. It is not that obvious that her car was the instrument of destruction.
But all it takes is a momentary inspiration to ask" You don't know anything about it do you?"
"No--of course not!"
Then the blood will be pounding in your ears.
You will be at your worst when the subject of her accident comes up, (as it is likely she will complain about it for a long time) your best bet is to freeze and say nothing. Silence can mean anything.
If she ever owes you a favor (cultivate this, if possible) then you can own up and say we are even.

Well there must be some damage on the car you were driving to smash a headlight.

Yes

yea... they'll know, there will be some kind of mark on your mom's vehicle.

Corner damage is really expensive. insurance will not cover accidents or damage involving two vehicles in the same household.