They call a land cfg like you describe a "flag lot" here, and, if it is a huge area, fencing would, of course, be really nice if you can afford it. Depending on the 'codes' for fencing, you might be able to fence directly to the house if you are looking to be able to just open a door or install a doggie door and have your babies safely enter a fenced area directly from the house instead of having to cross an open area to get to the kennel.
It you do not feel you can do the work yourself, you could call a fencing contractor...they could give you recommendations, too. Some kinds of fencing are pretty easy to put up...the kind that come in panels, but you did not say what kind (that I remember

) of fence you would be interested in. A 10x10 offers 100 sq.ft, which is probably sufficient for sunshine and potty, if regularly cleaned. It may not be a great amount of 'run' space; considering that they potty there, they may not want to run in it...not sure if yours are 'squeamish about stepping in potty, or if they are 'neat' and use the fence line like my Yorkie-Poo used to do, etc.
Were you wanting to move the kennel because of the distance to it from your house, or were you thinking of relocating it around the available yard space for cleanliness or the area, or...?
If you do fence, you may want to keep the driveway out of the fenced area to avoid possible accidents. Plus, unless the kennel would be in the way of the fence, would you need to move/remove it to install a fence? What do you use your yard for? Would there be party feet that would make keeping the kennel for the safety of the fur babies desirable?
I agree about tie outs being inappropriate. Yorkies are too small to be on unsafe tie outs in unfenced areas.