James IV of Scotland and I of England will be crowned alongside his wife. He ain't gonna be no "Consort" and it would be insulting to him personally for anyone to have the balls to suggest it. This is NOT the Aragon/Castille situation where it was known the pair would be inheriting and the marital contract (actually, I think they wrangled about it even after the marriage, but it started before); this is not the situation where a reigning single woman (Queen Mary of England) negotiates a marital contract (pre-nup in our parlance) to avoid her husband having control over England. This is an unforeseen situation where a woman NEVER expected to rule has inherited the throne unexpectedly and she's already wed to a King. Margaret had no training for the position of Queen Regnant, she's going to have James crowned right alongside her for a number of reasons: she NEEDS him to help her rule unless she's going to hand power over to a council; he can keep the child (I think Arthur is the only one she has at this point); it's no stain on him to take another mistress with Margaret in England, but that current only runs one way in the 16th century) if he isn't crowned (and unlike women, men are not 'crowned matrimonially' - ask Prince Philip). Margaret will then be in the position her OTL niece Mary was in: no heir (presuming son Arthur dies on schedule in 1510) and no way to get one (if he's in Scotland and she's in England...…). James IV can name anyone he wants to succeed him (Lord knows he's got enough bastards to chose from, not to mention cousins); but she's got only a younger sister, also not trained in ruling.
James died in battle, he's not above a fight over this issue. While Margaret's father didn't die, he was willing to over the same issue: the Kingship of England.
I'm not sure Margaret Beaufort's health will allow her to make any real decisions; H7's death broke her. Having first H7, then H8 die and the next heir wed to the Scottish King, she may well recommend uniting the countries - that was the point of wedding her granddaughter to the man in the first place. (It was just expected to happen in a later generation.)