re: Would you sell a future neighbor a 15'x70' strip of the edge of your property?

Well, that settles the unity of title issue, which I ASSUME LA follows.

Have you verified the lot can even be subdivided and a residence built on it?

Personally, given the fact it is free land I don't think I would personally be concerned about using an easement of necessity even if the property is subsequently sold but it does have potential issues and may have a negative effect on the value of the home once built.

Have you considered buying the strip from your families lot vs the stranger's lot? If your family won't sell it to you then a stranger is an even more uphill battle. Personally, I would require a hefty bit above "fair market" to sell off a strip like this if it were mine. You also have to consider the negative impact building on a lot like this will have on the value of a house you build. Based on the drawing and trying to scale it out from the 70' you need to for a driveway unless you plan to build a cracker box it may be shooting yourself in the foot.