How to correct highly influencing senior manager/client/customer

Been there, done that. Never easy and not always successful.
First, keep in mind that if this person has been in the organization longer than you have, others are probably already keenly aware of his or her style and have been working around it. If you are a temporary PM (like a consultant) you can't fix everything. Here are some techniques I've used - with varying success:
1) Facts, facts, facts. You refer to the senior manager as ignorant, but I think it's part of the PM's job to educate them. I don't mean argue with them but whenever I can I boil things down to facts and make sure the team, if not the manager, knows the facts.
2) Don't leave it to the senior manager to communicate. If you want him or her to send an email to the team, send a written suggestion so they don't have to figure out what to say. Same thing with presentations. Write out what you'd like for them to say "as a courtesy because you're so busy".
3) As much as you can, limit the time that available to the sponsor for communicating with the team as a whole. You want them looking to you as the PM - not to the sponsor. On my projects the sponsor is welcome to visit but not to attend weekly team meetings for that reason. "You're paying me to manage this project. If you come to the meeting everyone will look to you, because they respect you as the VP of doo-dah. I'll be glad to meet with you after the meeting, and there are definitely some times we will need you there. I'll let you know when..."
4) Over and above everything, work to develop a good relationship with the sponsor. Work to learn from that person - what makes them tick? why does he or she hold the opinions that they do? Keep in mind that when you disagree, YOU might be the person who is wrong.