Yes. It has come to this! PTQ sounds better when loud, so the sound's been gradually rising, and the C.O. has had enough!
So it's insulation or back to a digital piano other than what i have . . . Insulation suggestions welcome!

All I can say it is hard. Effectively you need to put a second wall in with a min 5cm gap between the original and new wall which you fill with sound insulation material. The best material is heavy. It is never going to be cheap.

I've had two different neighbours with a shared party wall and they've just been loud. Spent over £10,000 on sound insulation and all we were able to do was go from hearing their constant arguments at the top of the voices to hearing a muffled argument. It was a considerable improvement. But you can easily end up spending a small fortune and still there just needs to be one sound bridge and the sound gets through.

To be effective it should be on the wall surface where the noise is generated, not the back of that wall.

My music room wasn't particularly designed with this in mind but this is what I did:

The ceiling is underdrawn with plasterboard and there is glass wool between the beams. The walls are all plastered with glass wool behind the plasterboard. The wall opposite the piano lid, which therefore gets most of the sound, has a large tapestry hanging on it. I covered the existing floorboards with another layer of tongued and grooved boards. The piano sits on caster cuos on a carpet. The drum kit is on a very thick carpet.

It all helps.

You might want to look at something like Soundfold. It's not cheap but it looks pretty and works quite well. (My theatre auditorium is lined with Soundfold fabric.)

The sound tends to propagate also through the ceiling and the floor (depends how it is built). So to be 100% effective, you would need to create a box in the room... the cost is very high, not mentionning visual impacts. Unless for professional reasons, it is rather difficult.

A few questions,

Are planning to modify your house yourself or hire a contractor ?
What is the wall between you and your neighbours ? Simple drywall, brick or concrete ?
Or you can try to put a few sounds panel in the room with a rug under the piano.

well, I was thinking of a heavy curtain against the adjoining wall and a second adjacent one. Or, maybe, 2" or 4" expanded polystyrene sheets plus the (velvet) curtain, double glazed glass units were in my mind. Dammit, it's only a small room!
After looking at a few options online, I was starting to think "g'bye piano! Hello Harley . . . "
Now, I know many dps have acoustic control where you can achieve a "nice" sound fairly quietly without loss of timbre. . . .
Seems there are few cheap options left in this world!
Getting drunk certainly isn't . . . .
I know! I'll get the wife a job . . . .

Hmm, I'm not sure that polystyrene and curtains are good for soundproofing.

https://youtu.be/r6gPmWtXdlE

I made something like this for my piano room.

That's not going to help with soundproofing at all, but will help with treating the sound in the room. With or without these acoustic panels, he would still need to find a job for his wife!

I believe echo has a big effect on *perceived* loudness.

If that's correct, in a big room then putting curtains would help

Curtains also dampen high frequencies pretty well

What also helps is removing the contact between piano and floor eg with dampened castor cups

Curtains are bad at damping lower frequencies. Thad needs mass, as mentioned you need a heavy box encapsulating the sound and the box must have no direct contact points with the room.

I've had an idea. I use external hifi speakers, sat obediently beside my feet on the concrete floor which is carpeted. They point towards the wall beyond which sits The Adorable One. And the dog.
Now if I was to turn them 180 deg, they'd point to the wall against which the piano fits. That back wall would nicely (or otherwise) reflect the sound back to me from around the piano and the effect would be less on Her. And the bitch. Allegedly.
I might if this proves feasible, enclose the lot in a New Cabinet which would tidily clear everything up and enable the sound to emanate that coming from an upright.

Ahhh!! The joys of having little better to do!

Just to let y'all know. It worked. She. Is. Happy!!!!!!!