You're always up for a challenge in the thirst for knowledge, Tish!
I'm really like your results (the motion blur adds so much to the whole holiday atmosphere), particularly as you hadn't taken this type of image before!
I don't know quite how to follow the excellent advice that Pamela has given you!
When I take inside images with flash(external flash):-
1. I usually use aperture priority(f 8ish or the smallest I can get away with to get a reasonable depth of field - particularly when taking a two person portrait and I want both sets of eyes in focus).
2. Increase the ISO up to minimum 800( to try to achieve a shutter speed fast enough to avoid unwanted movement).
3. Set my flashgun to manual and experiment with the exposure levels on the flashgun to achieve as good an overall lighting effect as possible.
4. Take a few shots until I am happy with the results - a bit of trial and error in some respects but it does work.
I have to say that I do tend to use a tripod and, when I use the above method, it is usually for posed photographs - I also use the 10 second timer on the camera so I can make it on to the picture!!
Must get a wireless remote, sometime!
I know you probably wouldn't have had time to experiment in this circumstance but you could consider this approach for the future.
Pamela's White Balance advice is excellent and one I need to remember!!
Hope this is of some use to you, Tish!