I have a Thomas Jefferson Vanderslice in my database who might fit the one you seek. I don't have a birth date for him, but his brother John Henri was born 4 Mar. 1802. Other known full siblings were Daniel and Mary. The father of these children was Daniel Vanderslice b. 17 Feb 1759, at Providence Twp., Pennsylvania. According to an unpublished manuscript compiled by Samuel W. Pennypacker, later governor of Pennsylvania, Daniel Vanderslice was "b. 6 p.m. Feb. 17, 1759...Wigmaker on 5th street below Race, Phila.By his first wife he had Catherine, Joseph and Abbe. By his third wife he had Daniel, Thomas, John, Mary.He was a sergt. in the 9th Penna Regt. from 1777 to 1780 and was discharged about Ap. 1, 1780." Pretty specific information, which leads me to believe SWP had contact with someone with the family bible and first-hand knowledge of the family.
I don't have the third wife's name, unfortunately, nor do I have any further information about Thomas Jefferson Vanderslice. In an interesting coincidence, this Thomas's grandmother was named Catherine and I noticed that Daniel and Catherine are the names of two of your ancestor's chidren. Another interesting coincidence...the Vanderslice line that I've been researching the last couple of days were fishermen (sailing up and down the east coast from Philadelphia and some piloted ferry boats between Philadelphia and Camden, New Jersey. I suspect this may be the same Thomas and that he left Pennsylvania 40 years before the manuscript was compiled in 1880, and did not maintain contact with the family, thus SWP had his name linked to his father but no further information about him.
If you'd like to see where Thomas fits into the Vanderslice tree as compiled by Gov. Pennypacker, please take a look at my tree at RootsWeb's WorldConnect website. In the field that is labeled "Jump to specific database" just enter the code: 123103sjThis will take you directly to the index for my database.