OK, I think I have a way of doing this:
Phillippa was the youngest daughter of Henry Bolingbroke, or Henry IV of England. She married Eric of Pomerania, King of Denmark, Norway and Sweden. Henry of Monmouth, later Henry V was intended to be married to Eric's sister Catherone. Queen Margaret, the Nordic regent didn't want to involve the Kalmar Union in an alliance that could drag them into the Hundred Years war, so this wedding never happened. But if it had, there is a possibility that a child from this marriage could become king of England, Norway, Sweden, and Denmark. Hmmm... this is shaping up to be a timeline I should write. Anyway, with this POD, here's what the Grand Kingdom of the North's coat of arms could look like:
Argent a cross voided Gules, in the first quarter, parted quarterly, in the first and fourth quarters Azure three fleur-de-lies Or, in the second and third quarters Gules three lions passant gardant in pale Or armed and langued Azure, in the second quarter Or three lions passant in pale Azure crowned and armed Or langued Gules, nine hearts Gules, in the third quarter Azure three sinisterbendwise streams Argent, a lion crowned with an open crown Or armed Gules, in the fourth quarter Gules a lion rampant Or, crowned and bearing an axe with blade Argent, the inescutcheon Azure four crowns in square Or.
The arms is based on that of the monarchs of teh Kalmar Union, and is for the ATL king, son of Henry V and Catherine. It has quarters for the four kingdoms (England, Denmark, Sweden, and Norway), with the symbol of the Kalmar Union modified for four kingdoms rather than the OTL three.