Which flash? Please advise

Have a look at the Metz 58AF1. It sells for £255 and is a very powerful and versatile flashgun. It dedicates to the K20D with PTTL mode. The flashgun also has its own Auto mode and Manual. Its capabilities are vast, so allow time to read the manual. Take it a step at a time. I have had this flash for almost 2 years and am very pleased.

The only other dedicated flashgun I would recommend would be the Pentax 540FGZ, but it is a lot more expensive.

One more vote for Metz 58AF-1. Far the best value for money.
KZ

Not to discourage you from acquiring a good flash, but why not consider getting an appropriate lens for this "job"? With a K20D you should be able to use a reasonably high ISO and SR, so an f/2.8 lens might well be enough to handle performances, with the additional benefit that you'll be OK at venues that require "no flash photography".

Personally, I use a Tamron 28-75mm f/2.8 (constant aperture) for most performances, backed up with a Pentax 50mm f/1.4. In full-frame terms these are 42-112.5mm and 75mm f.o.v. equivalents, so they're long enough for many situations. Preferring zooms, I generally stick w/ the Tammy unless the lighting is too low, in which case I move to the 50/1.4. These are realistic suggestions, at least in USA pricing terms, as the Tammy sells for a bit more, the Pentax for a bit less, than the price of the Pentax flash,(which is not very much more than the Metz here). Plus, you might find either lens used for significantly less. (Earlier, manually focusing, f/1.4 or f/1.7 50mm lenses could also be considered, as these fast lenses focus easily, even in lower light, because they're so bright wide open.)

If you'd like to see some performance photography mostly taken w/ these lenses, you can look at link The shots of the Sweeny Todd performance are all with these two lenses. (In case the link doesn't work, you can type in "http://www.flickr.com/photos/barbaranavi/sets/72157609216507083/").

Don't forget to enjoy the play!

I'd recommend the metz 36 or 58. Great priced lenses for the capabilities. You'll find many comments in the forum with regard to these flashes if you are interested. Good luck and happy shopping

BrooklynBoy has the best advice I believe.
Most of the time you aren't even allowed to use a flash on stage and a flash is only useful at a certain distance since you said quite some range I think you would need quite a lot of power.

Before you spend money on a flash or a lens, check whether you will be allowed to take photographs at all. Photography is not generally permitted at theatrical performances, be they professional, amateur or school. Flash photography will almost certainly not be permitted during the performance.

I'm with the fst lens advice here. Why should you spoil the rest of the audiences enjoyment by popping off a flash?

How far away are you from the stage and what would your budget be when talking about a lens?

We try our best

For the lens the DA*50-135 or Tamron/Sigma 70-200 would do quite well.
Those are constant f/2.8 lenses and with iso800 you would get very far.
Problem is though that those lenses are expensive.
Tamron 28-75mm F2.8 will also do very well if you're not too far away but that one also cost almost twice the amount you want the flash for...

I'm not so good with second-hand lenses but the Pentax 135mm also aren't that expensive I believe. Problem is though that it's a fix focal length so chose your seating wisely then.
A 50mm lens might also do the trick but I think it might not be long enough to make photos of just your granddaughter, you could of course use it together with the 135mm and maybe even a 28mm lens.
You might go a bit over budget then with 3 lenses but probably not much and you can cover quite a range then.

The Metz 58 is a superb piece of kit.

Whatever flash you end up buying, make sure it has a AF assist light so your camera can focus in absolute darkness. (if there is something to project the pattern on...).
I use my flashgun quite frequently in SB mode which turns off the flash so that only the AF assist function is working, this is allso great when using a fast lens.