We just purchased a home which has an easment on our driveway. This did not show up in our title search, but has shown up on the plat.

The neighbor that has this easment does need this to access their driveway.
That I do not have a problem with.

My problem is they are using the whole driveway, allowing their children to play on the driveway. And they are also parking in my yard beside the driveway.

I have went to the county records office to find an actual recorded easemnt and the clerk could not find one. The only records we can find is the plat.

Their easement on my plat states this:
20' Perpetual & Excluxive Easment for access

My questions are:
1) Can their childen play on my driveway? If so, if they are hurt will I be liable?
2) Does easement for access mean that that is all they are allowed to use it for?
2) How can I stop them from using the whole driveway and my yard beside the driveway
3) Does exclusive mean I can't use that part of my driveway? If so, shouldn't they have to pay for the upkeep and taxes?

I really try to be a good neighbor and I'm trying to determine my legal rights before I contact them regarding this.
It is better for all of us if we try to get along.
I am really worried about my potential of being sued should their young children get hurt. They are around 3 or 4 years of age, and she just lets them roam with no supervision.