Oh yeah, that was a thing IOTL. But Jane was older and had a thing against people who wanted to control her, no thanks to her mother Frances. Would Margaret do the same?
Since we've already discussed what happens to the sisters when Mary gets the crown, in the scenario where Margaret gets crowned, what happens to Mary and Liz? The Tower?
To be fair the idea that Jane Grey's parents were dictatorial and a couple of bully's is now largely discounted - it was based on a letter by Jane to her Roger Ascham - he himself was using it to promote the idea that gentle treatment better encourages children to learn - to be fair the letter could have come from any highborn bright Tudor child moaning about their upbringing. Ascham himself later wrote kindly of both Frances and her husband. There are other letters talking of Jane's piety and her closeness to her mother.
Frances herself is reputed to have opposed the Dudley match (on the grounds Jane could do better than a mere younger second son - her parents had previously thought to marry her to Somerset's heir before his fall).
Moving on - in the event Catherine Tudor succeeds to the throne as the law dictated - then Northumberland has to deal with the issue of her half sister's - Mary is heir presumptive followed by Elizabeth - if both accept their younger sister's accession - then I suspect both remain in the country on their respective estates after their sister's coronation - both were wealthy (Henry left them well provided for) - neither can marry legally without the consent of the council - both represent a danger if they are married outside the country.
Mary will almost certainly continue to attend and hear mass and enjoy life, Elizabeth will outwardly conform as she did under Edward - both will probably resent making way for the younger sister - both are too clever to make a major blunder in the short term.
Mary will probably prove a focus of Catholic discontent and rebellion as in this scenario as Cranmer is likely to continue to transform the English Church into a more Protestant one - imagine a Wyatt rebellion with Mary the alternative - assuming any rising is defeated then its the Tower for Mary and tighter restrictions on her... I think the Council will hold of putting her on trial especially during her sister's minority (presents many of the issues that Elizabeth did to Mary's council) - her health will probably decline and she may well die as in OTL before her sister is of age.
Edward VI was highly influenced by men like Cranmer in his religious focus - it is not unlikely given her background that his younger sister might be similar in tastes - and she is now in education terms under the control of those same men.
As to Queen Catherine's household well certain key figures will have significant influence I would expect Catherine Willoughby Duchess of Suffolk to be a key person about the Queen (she was very close to Catherine Parr in her lifetime, was a devout Protestant and despite her second marriage was widely respected) with her comes her stepdaughter's and granddaughters (the Grey's) and her own children by her second husband. (In OTL she went into exile under Mary and her children did well under Elizabeth )
Assuming Mary dies in the late 50s then Elizabeth is heiress presumptive until the Queen produces an heir - some might consider her to have more right - but with a Protestant undoubtedly legitimate Queen Regnant there is little incentive to replace one with the other...she may well be close to her half sister and might be visible at court - second in rank to the Queen etc. Privately she might resent making way for the younger but i think she'll live with it.
As to Elizabeth's marriage - if the council is desperate for a foreign alliance one might be considered and Elizabeth would be an option but a risky one if the husband is too powerful (once Mary is out of the way he might think his wife has more right to the crown) - I think it likely keeping her home is the sounder decision until the Queen is wedded, bedded and delivered of an heir.
The young Queen is going to be an attractive match - but a Catholic match would prove extremely difficult for her - if she has the Tudor pride (like all her siblings) then a match with someone too low born isn't going to attract either.