I have never seen any original sources listing the names of John Bodine and Mary Crocheron's children. As far as I can tell, the best list of these children would be John, Isaac, Jacob, Sarah, Catherine, Peter, and Abraham. However, one should realize that this is only an educated guess. Hopefully, more information will come to light on who John and Mary's children were, but it is not likely. These children were probably born on Staten Island, but there is no source for this information either.
Info from Theodore A. Bodine says that she later married Isaac Van Meter. Henry Mulliner appointed Adrian Mulliner (Molenaer) and Isaac Bodine as executors of his will. Adrian was probably his brother and Isaac must have been Catherine's brother.