A photo of the overall area in question along with a closeup to ID the groundcover plus a description of goals would be helpful. What you can do versus what can be accomplished successfully are two entirely different things, and with current information any suggestions will be wild guesses.

I can send a picture when I get home. It is growing like crazy & we want a more simple look. Would any kind of ground cover be able to penetrate a plastic barrier?

Hmmmm......groundcover is typically planted because it does provide a very simple look. Most mass plantings of a single plant species do just that.

And yes, some groundcovers will not be stopped by plastic. Those that tend to grow by rhizomes or stolons will just continue to grow to where the plastic is not present and pop up there.

Often when you have ground cover someone put it there for a reason. What is it, where is it and what do you want to replace it with?

We put plastic over our ground cover to try and kill it and then mulch on top. Don't want to use pesticides because we want to replant in the garden.... Well the ground cover survived and grew through the plastic. It will not die. I rip it alk out every year and it comes back no matter what. It's a fight that never ends. It chokes out my other plants. This year I'm planning on launching a full attack.