The Battle of the Seedlings... Can I win?

Question:Is there a way to prevent new seedlings from popping up EVERYWHERE? They're in my garden, they're in my planters, they're along the fence line. Every time I turn around there is another tree! The ones along my fence line are almost impossible to keep down. I tried pouring almost an entire bottle of some stuff that was supposed to kill them, on two that were coming up by my house. They came back this year again! Only they look like Trees from another planet! The leaves are mangled and twisted and instead of being spaced out they are so full it almost looks like a bush.
Is there some sort of treatment I should put down in the winter or spring that will stop these things?
Whats the best way to kill the ones I don't want ,which is pretty much all of the ones that are coming up now,? Obviously the stuff I bought wasn't the answer.
THIS IS WHAT I BOUGHT:
Roundup® Poison Ivy & Tough Brush Killer Plus Ready-To-Use

Kills all types of tough weeds and tough-to-control brush

Answers:
It all depends on what type of seedlings are popping up. Most common are maples, but a simple mowing with the lawnmower is enough to kill most of them. If the sapling is a couple of years old and cannot be pulled from the ground, what you are doing with the chemicals will work, but it will take several applications until you can kill them off completely. Roundup is meant more for green stemmed plants than trees, but I did use it to kill off a mulberry tree that was growing near my house's foundation. And like you mentioned, the leaves were contorted looking after the first couple of applications. About the 4th try, it worked.