Re: Arbella Stewart- with a POD in the early 1560s there's no guarantee she'd exist (her parents only married in the 1570s). With no marriage to Mary her uncle Darnley won't get himself killed in the same circumstances, and could produce children from a difference marriage.
The Lennox Stewarts also disputed the Hamilton's status as next-in-line to the Scottish throne (there was something iffy about the 1st Earl of Arran's marriage), so they could get drawn into disputing the throne in Scotland, and that would presumably affect their prospects in England.
Things in Scotland could also get complicated if the Hamilton heir goes crazy, as he did IOTL.
Re: the succession in England. With Mary off the table you're down to, what?
- The Greys. Catherine has already disgraced herself with her secret marriage at this point (I think). Though she is the most respectably Protestant of the claimants. Mary is deformed.
- Margaret Douglas and her kids. Though Darnley is a pretty loathsome character who might do something stupid. Charles may have had delicate health. They may also be suspect religiously.
- Margaret Clifford (daughter of Eleanor Brandon), and her Stanley kids. They had their own brushes with disgrace and Catholic plots IOTL.
Another question- without Mary's imprisonment, do we still get something akin to the Northern Rising, and does Norfolk still get himself executed?
Aren't there potentially hurdles to them succeeding based around Henry VIII's will and Darnley's
difficult character?
The 1st Earl of Arran's first marriage was dissolved due to the fact that it emerged his wife's first husband had still been alive at the time of their marriage. If that wasn't the case then his second marriage would have been regarded as invalid and his issue illegitimate.
In that case the claim passed to Mary Stewart's (dau of James II) younger children's descendants including her great grandson Matthew 4th Earl of Lennox.
With Mary out of the way - Arran would in my view have been King - he was widely considered the strongest claimant and Lennox was a rebel living in England. Arran was probably a good choice for the Scots - he himself wavered between Protestant and Catholic (but at this period was firmly allied with the Lords of the Congregation) and his daughters were married to some of the most prominent Catholic families including the Huntley's.
His heir was also at this point on the reform side - he would however be declared insane within a short period and was largely held under close watch for the rest of his very long life - he was eventually succeeded by his brother John's son.
There was a strong streak of mental illness in the family Arran's wife and her sister were considered to have "issues" as was Arran's younger son and one of his daughter's.
So assuming Arran becomes James VI in 1561 ish and is on his death succeeded by mad King James VII it is likely the country faces a long long regency under Prince John Duke of Albany one assumes.
Interestingly at this point all of Arran's sons are unmarried.
As to England:
By statute at this point the succession:
1) Lady Katherine Grey - her illicit marriage is suggested to have taken place in December 1560 - by her husband she bore two son's but the second might be butterflied by Mary's death changing circumstances
2) Lady Mary Grey - her own low marriage didn't take place till 1565.
3) Lady Margaret Clifford Countess of Derby (daughter of Eleanor Brandon)
4) Ferdinando Stanley Lord Strange b1559
5) William Stanley b 1561
Notes: Katherine's illicit marriage was declared invalid however her claim to the throne was widely recognised at court at this point and indeed at the point her marriage was discovered and her obvious pregnancy a pamphlet suggesting she had the strongest claim after the Queen was published.
By Primogeniture:
1) Margaret Douglas Countess of Lennox
2) Henry Stewart Lord Darnley
3) Charles Stewart b1555
Then the Grey, Clifford and Stanley claimants above.
The problem for Elizabeth is that she personally disliked all of them - she had little time for the Grey girls and had a difficult relationship with Margaret Douglas. I suspect her councillors will favour the Greys in the short term and if they behave as in OTL then opt for Margaret Clifford - unless Darnley disgraces himself and the Queen can effectively adopt the young Charles and have him raised in effect as her adopted son and as an Anglican. Then assuming he lives longer than in otl its Charles I in 1603