Balancing fill flash with ambient light

I want to take a portrait photograph of my mother and father, individually sitting a the dining room table (doing a crossword/jigsaw puzzle) yet still have the garden through the dining room window acceptably lit (their garden is a huge part of their interests).

The above will require a balance of ambient light in the garden and fill flash in the dining room. The following is the result of a trial run (a proof of concept if you like) this afternoon (02/02/2014), in the lounge, rather than the dining room - the actual posed photos will be taken when the back garden is a little more green (it's currently winter).

First, I take a camera meter reading off the driveway across the road in Av mode (aperture priority) at F4:

ISO 400, f4 1/30th no flash
 
At ISO 400, the camera suggests a shutter speed of 1/30th of a second.
 
The camera is now set to M (Manual mode), ISO 400, f4.0 and 1/30th of a second.
 
The shot is recomposed on the vase of flowers and another test shot is taken:
 
ISO 400, f4 1/30th no flash
 
As expected, the outside environment remains correctly exposed, but the flowers are under exposed quite considerably.
 
A flash unit is fitted and turned on, set to full power (1/1) and zoomed to 80mm (the lens is zoomed to 82mm). A light/flash meter is set to a shutter speed of 1/30th and held in front of the vase of flowers, pointing toward the camera. Still in M, f4 & 1/30th, a shot is taken:
 
ISO 400, f4 1/30th flash 1/1 power

Wow, over exposed or what ?
 
The reading on the light/flash meter reads f20. The camera is set at f4. Time for a little maths... ok, we can count on our fingers.
 
Seriously, on our fingers we count from f4 to f20: f4 - f5.6 - f8 - f11 - f16 - f22 (near enough) I make that 6 fingers, or if we want to sound as if we know what we're doing, 6 stops.
 
On the flash gun, we reduce it's power six times: from 1/1 - 1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64.
 
With the same camera settings, another shot is taken:
 
ISO 400, f4 1/30th flash 1/64 power
 
I thought that was a little on the bright side, so I reduce the flash power one more stop to 1/128:
 
ISO 400, f4 1/30th flash 1/128 power
 
 
Much better :-)