I know it was a common practice, but I don't think she came later. If she did it would have been very soon as James landed in New York May of 1812 and their next child was born in Washington Co, NY on 11 Jun 1813. From 1807 until 1825 there is about 2 years between children, as was common in those days, and they didn't seem to miss a beat.LOL
I noticed the count of passengers was way more than count of names that appeared on the ship's passenger list, again leading one to believe names of his family just not shown.
My husband has ancestors where first child was born in England then a BIG gap before next child is born in the US. Pretty obvious he came ahead and she and that first child arrived here much later. The three children born in the US are fairly close in birth years, helping to prove the "husband came first, wife came later" theory for them.