Dale, I don't understand your argument about a Beatrice, wife of David. I also don't understand when you talk about two Davids with the same father but different mothers.
There was not a Beatrice, wife of David. David's wife was Alice Martin.
There were not two Davids. There was only one. His name is spelled David in modern English. Daffyd in Welsh. And sometimes Daffid in early records.
I haven't yet been able to trace the supposed Latimer marriage. I'm still looking, but it's likely that will be a different William.
One thing you should understand is that these are all gentry families.
Whenever you mention the washer woman / laundress I wince a little. For armies in Tudor times, washer women were basically prostitutes who followed the army. One of the ways of justifying their existence was that they did chores for soldiers, including washing and nursing. Many of the washer women at the Field of the Cloth of Gold would have been French women, converging on the event. There would have been some English women too, but they would have had to ship over for the event. Probably not worth the price of passage for many. Certainly, only a few favorites would have had a temporary romantic attachment to an officer that might have let them hitch a ride on a military ship.
There would not be a noble woman in charge of washer women. Washer women were probably organized from their own ranks and commanded by the sutler, who told them where to camp, etc., according to military convenience and necessity, with due regard for the convenience of having them around.
If Henry VIII truly had a dalliance with a washer woman, it is unlikely he would have believed that her son was his. Unlikely that any report of the birth would get through the bureaucratic wall around the king. And, unlikely that even Beatrice would have known the father. There would be no favors, no political preferment, no coat of arms from a royal half-sister. Just an anonymous baby growing up in poverty somewhere.