In response to your question,"Did Adam or George have a brother or uncle named Bartholomew?" The answer is definitely, no.
Although there is a direct link with Yeagleys in Northumberland County, PA, through Adam's grandfather's brother George, and very possibly one to Yeagley's in New Jersey, there is no way to prove that Bartholomew, or the Revolutionary War soldier from Somerset, NJ, Adam Yeagley, were directly related to Adam (b. 1812) Yeagley, and the South Lebanon/Yeagleystown Yeagleys, from which I have descended.
There is also no way to prove that John Jacob Yeakley, Adam's grandfather, was born in this country, came here with a parent (although Hans Ulrich Yeakle is highly suspect), or, came here alone or with his brother George Yeagley.