He's on a Magna Carta trail, so the first thing is to see what Richardson says. Richardson has uncovered a lot of sons and daughters that aren't in other books, including Mowbrays.
But he's not in the online preview, so you need somebody who's got the book.
In general, there's nowhere to look for a complete list of anybody's children. New ones are discovered all the time. Everybody's wife is somebody's daughter, and a lot of medieval daughters are only known from a statement that somebody married them.
It all depends where you find that statement. Lawsuits and property deeds are good. Links that appear on the internet by magic, zillions of those, not so good.
The really hard cases are the old family pedigrees. They contain a lot of genuine wives and fathers-in-law that are unlikely to be confirmed from any other source. They also contain a lot of names that were just made up to fill gaps. Then it's a judgement call.