See, that’s an easy question and should have been the question to lead with.
What do you think of my idea to have Rodolfus get his plan back on track by breaking out of Azkaban and putting Delphini under Imperio?Now what?
First, the party + Delphini have a plan, now they need to implement it. I can think of any amount of challenges to trying to implement a plan that causes major changes to the past.
Now villains. You no longer have a big bad, so you will have to replace her. How about time elementals, beings responsible for maintaining the time stream who attack the heroes during the mission and afterwards.
Of course, depending how evil/cynical the DM is, the players’ good intentions could result in a bad future. It is a common time travel trope for a reason.