Easement nightmare, need sound advise please?

In August of 2007 we purchased a house and 10 acres. (Missouri). In August of this year the person who owns 1/3 of a 10 acres that is located directly behind us came to the house and told us there was an easement through technically through our front yard to his property.
Now here's the deal, our property fronts the county road and is surrounded by 3 individual property owners on each side including the owner that's claiming he's got an easement. How he came about this property is through his step-father and mother who surveyed the back 10 acres of the property I own off and kept it and the kids inherited the 10 acres when she passed away.
Our property was bought at auction, private auctioneer, not taxes or a forced sale. The auctioneer specifically stated that there is no access to the land behind us from the land that we bought. Nor did the owners that we purchased the place from state there was any access from the front 10 acres.
I have checked my title insurance, legal descriptions of both properties and with the recorder of deeds for our county and there is no written exclusions, inclusions or easements on either legal description except for utilities. BUT, some friends in Real Estate looked on a plot that they have in their office and it shows a broken line going about 3/4's of way across our property with no explanation of what it is.
At the time of sale, and at the closing there was no verbal conveyance of an exsisting easement, nor was I provided anything but the title insurance, legal description and all the normal paperwork that's given at closing. Not one thing indicating an easement anywhere.
Nor have the owners of the property behind us helped in anyway to maintain this easement if it even exsists nor have they used it until last month.
Here's the deal, I am more than willing to give them an easement, but I want to choose where it is located and obviously it will not be through my front yard.
Do I have the right at this point to deny them access until a fair agreement can be reached? BTW, access was granted the first time by a tennant on my property that I was unaware of. I want to keep things on cordial terms in the hopes that may be able purchase the property at a later time. The owner has offered it to me, but right now the price is unreasonable.

I forgot to mention, the survey was done less than 10 years ago, in the survey there is no mention of exclusions, inclusions or easements, nor or any marked. My property boundries are clearly marked by the survey company.
On my owners policy there are no easement statements except that of the utililites.
I have no intention at all of landlocking the owner. But, the auctioneer made it clear there was no access on my property. Nor are there any paths leading to the back property.
I give them access, just not in my front yard. Off to the south side of my property there is a perfect access that will not disturb my family or be a danger to my kids and pets that are playing in the yard.
Hope this explains this better.

Easement may have been granted as an easement appurtenant to one of the past owners and not be obvious on your title or deed. A competant title search should reveal if at any time there were such an easement granted; you might do well to hire a full search on the neighbor's property with an eye to finding the ROW. In most state law, it is illegal to landlock a property; but that does not mean the owner of the lot in question can place an easement. In addition you state "title insurance"; if you have an owner's policy, the title company has some responsibility for locating the easement as well as insuring it; and if there is no easement,. they have a responsibility as well to defend your fee simple title rights.

I'd ask my closing atty, and the title company to sit down and look this over; and decide how to proceede

If there is no record of the easement legally recorded at the County courthouse, there is no easement. You can go to the county clerks office and they can help you research all applicable documents relating to the property.

You might look here:

http://homebuying.about.com/cs/easements...