Furthermore, when Charles II dies, would his son be crowned in Scotland as well as London, or simply have one coronation? Furthermore, do both Parliaments grant the King money or just the one?
The monarch is crowned in the two separate countries but were paid by the single government, due to the English government controlling all the money since Scotland signed over all its debt over.
Another question hanging over Charles III, is what to do with his father's bastards? His father, King Charles II, had fathered numerous illegitimate offspring by his many mistresses whom he acknowledged.
Also with Isabel Luísa of Portuga, she was the presumptive heir to the throne of Portugal between 1668 and 1689, so the English government would not want to marry her off fearing that the power they already share with Scotland, will have to be split again with Portugal, so would want to wait for Peter II of Portugal to have another heir, and between the birth of Prince John of Portugal on 22 October 1689 and her death of small poxs on 21 October 1690, only leaves a single year for her to travel to England, be acquainted and married, to then produce a heir.
What about marrying him off to a proud and Protestant, Her Serene Highness Duchess Sophia Charlotte of Brunswick-Lüneburg (Hanover), who is great-grand daughter of King James I, via his daughter Princess Elizabeth of Scotland who married Frederick V, Elector of Palatine.
Here would be my royal family.
Charles II of England (b.1630: d.1685) m. Catherine of Brazanga (b.1638: d.1705) (a)
1a) Charles III of England (b.1668: d.1722) m. Sophia Charlotte of Hanover (1668–1705) (a), Magdalene Graham* (b.1684: d.1747) (b)
1a) Charlotte, Princess Royal (b.1685) m. Louis, Le Petit Dauphin (1682-1712)
2a) Charles Stuart, Prince of Wales (b.1688) [Future Charles IV]
3a) Princess Elizabeth Stuart of England (b.1694)
4a) Princess Sophia Stuart of England (b.1696: d.1700)
5a) Prince Stuart, Duke of Kintyre (b.1698)
6a) Stillborn Girl (c.1705) - Died during the child birth with mother.
7b) Princess Catherine Stuart of England (b.1706) m. Christian VI of Denmark (1699-1746)
8b) Prince Frederick Stuart, Duke of Clarence (b.1705: d.1719)
9b) Miscarriage (c.1707)
10b) Prince Henry Stuart, Duke of Gloucester (b.1710) [named after his lost uncle]
11b) Princess Mary Stuart of England (b.1712) - William IV, Prince of Orange (1711-1751)
[*] James Graham, 3rd Marquess of Montrose