Both are likely, the later more so. She was pretty in love with Francis Stephen but will have to marry again if they have no issue. Say, their eldest daughter dies and Joseph II is still born. But I still doubt she marries just to keep Piacenza, considering her suitor at that point would've been Don Carlos... the future Charles III of Spain. If they had enough children it'd be fine, and I suppose her husband could be made HRE (well, it would be given practically). But I still think she might be pressed for a lesser husband. She was a strong woman and Francis Stephen, crudly speaking, was nothing to her. He owed all his position to her, ala Victoria and Albert. I think her advisor, Kaunnitz, would push for a similar union once the widow is torn from her grief and must remarry.
In the second issue, if the reigning HRE only leaves daughter, one of his daughters will succeed to the hereditary domains and her husband will be named HRE. The same exact situation you describe happened with Maria Theresa herself. Charles VI had a brother who left only daughters; a 1701 Pragmatic Sanction had been drafted to allow females to succeed in lieu of a lack of male, with Joseph's daughters being senior. Charles VI chose to override it with his own sanction giving Maria Theresa seniority and effectively denying her aunts any and all share to the inheritance: hence Bavarian and Saxon hostility and attempts to take their fair share.
Interesting. Maybe butterflies could move up Aix-la-Chapelle and the ascension of Don Philip to Parma-Piacenza, with Maria also asking for Genoa and Modena (I think? Maybe Mantua, can't remember) as well. Joseph would ideally still be a child or dead, leaving Maria in a situation where she's only had daughters by Francis Stephen and needs a husband to be Emperor. Alternatively, you could have Don Philip come to her court - maybe even to court one of her daughters - and she falling madly in love with him and marrying him out of love.
In the second scenario, I advocated the brother-in-law's succession in an occassion where the niece is still an unmarriageable child and the HRE's death is clearly eminent. Alternatively there's no niece and the popular brother-in-law is simply pushed forward as heir in the complete lack of alternatives (othe than the HRE crown passing completely out of the family). Maybe for his succession to go through Austria-Hungary would have to come to terms with others and incurr a few loses here and there.