When I worked in a publishing company my direct supervisor was demoted and I took his place. It was a bit uncomfortable at first, but then I realised he really didn't want the responsibility that's why he was demoted. We worked as a team and I would divy up the workload, I take a little more than I would give him and always tell him what I was doing as well as what I wanted him to do that way it seemed more like we were sharing, I wasn't dictating.

T tasteful,
A adroit, and
C controlled
T telling

I have no advice to offer, but I wish you good luck.

I would respectfully bring her in on those things that need to be fixed and work with her to fix them.

Damn... That's a tricky situation.
How far out is she until retirement?

This may sound just a little cruel in some ways...
But I would assign her remedial tasks that she couldn't possibly screw up.
And if she asks...
Respond by saying something along the lines of "You've done this for a long time. I want you to take it easy as you coast into retirement. You deserve it."

The people you will be supervising are the ones you need to worry about - this is the crew that will be getting the job done.
This could be a good learning experience, of course you are now aware of certain truths and that is a plus. Stay professional, keep emotions and ego out of it and get the job done as rapidly and error free as possible. Keeping the bosses above you informed will be to your advantage but don't brown nose. Good Luck.

Do the toilets need cleaning ? ......lol

On the one hand, it's true that offending her is not your primary concern, this is now your career and your new boss will not take "I didn't want to offend her" as an excuse for not getting the job done.

On the other hand, good man management skills are a MASSIVE benefit to your skill set. This would be an ideal learning opportunity, asking for advice is definately a good move, don't be afraid to ask for advice from people you admire and more experienced people in your organisation.

My old boss had terrible man management skills, my new boss is the complete oposite.

My only advice is to remain professional at all times, personal feelings and reactions will end in disaster.

Dunno, don't care.

Will she be making any contributions to the organization or just sucking the air out of the room? My experience tells me that she has little useful to offer from now on, and paying her for a few months of paid time off as a reward for years of service and for accrued vacations is probably the cleanest, least damaging way to end her time there. It's probably also the cheapest for the company.

Basically go along with her cover story, say you can see that the stress was getting to her and understand why she wanted to slow down, pass it off as burn out while cleaning up the mess and assign straight forward tasks to her with the instruction she is not to worry about anything else as it is now time for her to look after herself. Any time she starts interfering stick to that song sheet, cut her off at the pass and remind her that she has to look after herself and slow down.

Manipulative I know but she gets to save face and you get to get on with what you have to do.

Were I in your position I would be most concerned with getting the job done.
If She is offended by the new boss she can quit. Problems solved.

Assign her tasks that keep her out of everybodies way, ask rather than tell her,
keep her busy hopefully productive, but where she can't stuff up.

With good humor and tact, of course, which you have.

I have no idea, but am impressed with your kindness. Very rare in the world of business.

If you can assign her to specific projects to keep her out of your way... do it.