Agree as H8's Dowager Queen Mother, CP
Oh wait, sorry I was thinking of Howard.
Any way, there would be no chance of her being allowed to marry Seymour, since as mother to Edward's heir, she could be used to make the Seymours even closer to the throne if such a marriage took place.
Also, Henry's eldest daughters would probably stay with her and actually be given good marriages as they have another brother between them and the throne.
would not be allowed to remarry, but would stay at Court as Mother to the 2nd & 3rd in line,
I can envisage her being quite involved in her children & doing a reasonable job. Apparently she had good relations with Edward, Elizabeth & even Mary despite their religious differences.
Without the Seymour marriage and "geriatric" pregnancy she will probably live several years ... maybe a decade or more. Given her more Protestant views, evident in OTL in her mentoring of her step daughter Elizabeth, I can see her main influence being securing solidly Protestant heirs to Edward.
Mary would be near the end of a long chain of heirs, so no "Spanish Marriage" of Queen Mary to Philip II of Spain, which would change the rate of conflict between Spain and England.
In addition a more solidly Protestant England in the 1580s might affect the war of he 3 henrys in France.