Well I know THAT! Still, wouldn't many in England prefer Anne as a Protestant (if Lutheran) Regent to Ludovic, a Scottish (and is he Catholic?) Regent with a shot at the Throne himself should anything happen to those poor wee children?
Anne of Denmark wouldn't be around for the issue to come up: she had intended to be present at the State Opening of Parliament, so she would have been killed with the rest.
(source)
Ludovic Stuart was Protestant (Scottish Presbyterian). Anne of Denmark's religion isn't known for certain, but she's widely believed (both by her contemporaries and by modern historians) to have been a closet Catholic.
As i said above couldnt the scottish nobles declare Ludovic Stewart King of Scotland thus breaking the union with England if they exploit the disarray in the realm following the explosion?
They could have, but would they want to? Personal Union under the Scottish royal family was advantageous to Scotland as well as to England.
Ludovic's claim to the Scottish throne would have been very weak while there were still surviving children of James VI, and while his political position in Scotland was very strong, his political capital was not limitless. If he were to act too aggressively, he'd lose a lot of the strength of his position.
The most likely breaking point between England and Scotland would be over the regency, if an English regency council arose in rivalry to Ludovic. Groups that could do it might be whoever controls London in the immediate aftermath (probably the Lord Mayor, the Sheriffs of London, and the Constable of the Tower), or the guardian of whoever of Charles or Elizabeth has survived to take the throne (Robert Carey or Lord Harington, respectively), or some coalition of people with claims to be next in line to the throne (Arabella Stuart, Edward Seymour, and Anne Stanley). Probably one of the first two groups would proclaim a council, then invite the other to join.
In that case, there would be no need to crown Ludovic to temporarily break away from England. Ludovic could rule in Scotland as regent, and there would then be a diplomatic (possibly escalating to military) struggle over the guardianship of the young King/Queen.