As stated earlier, I have a folder called "To Be Sorted" in my Pictures folder on my hard drive.

Here's my workflow.
1. Eject card from camera, Insert card into MacBook Pro and Copy photos to my "To be Sorted" folder. Eject Card, do not format.
2. Open LR, import photos from folder. I know that you're not supposed to sort by date, but I do, and it works just fine for me. LR then moves (not copies) those photos into the correct file hierarchy.
3. Quickly Cull photos (out of focus, bad shots) in the Library module.
4. Switch to Module mode and do the rest of the editing and deleting.
5. Switch back to library mode, select the photos for exporting and save as high res jpg to my hard drive.
6. Backup both raw and jpgs to external drive (I should do this every time, but this step gets skipped until a have a couple weeks worth of work. I haven't set up my hard drive in our new house on our wireless server yet, so I have to physically connect it to my computer, what a PITA).
7. upload all JPGs to smugmug site.
8. upload select few JPGs to facebook.
9. format card in camera.
10. Go take more pictures...the cycle never ends.

My first thoughts would be to use a lower (200),aperture of 5.6 or 4 and disperesed flash of about 1/8 power. The thought is to get a shallower DOF (blurry background)and get light into the faces of the people. f5.6 or f4 should give enough DOF to keep the people in focus and give some seperation from the background. There are times to add your own light to the shot. Consider using a soft box over your flash gun. There are very few times when you should flash at full power, so turn it down (1/8 or 1/32).

Okey dokey, here's a go at it with what you do have. I used Elements 12, but all of this is also in Elements 11.

1) Image>Transform>Perspective Widen a bit at the top since you're still shooting up.

2) Enhance>Adjust Color>Remove Color Cast Put the eyedropper on the middle kid's white outfit and click.

3) Filter>Blur>Gausian Blur Set to 1.0 pixels. This may be counter-intuitive but the blur reduces noise and pixilation without affecting the final image, while sharpening makes noise worse.

4) Image>Crop 8X10

For the rest, I used Tapaz ReMask3, but you can do the same with PSE 11 quick select tool and refine edge.

5) I selected the entire family from the background (ReMask does this as a separate layer. In Quick Select, you'll first want to make a duplicate layer of the background then do the selection.) Then Enhance>Adjust Lighting>Brightness/Contrast. I maxed out the brightness (this is only affecting your selected area), then reduced the opacity of this layer to 50% to bring out the family from the background. Then merge that layer down.

Since the folks on the right are farther from the ceiling light, then I worked on each of them separately, except for Dad and the baby. With the girl on the right I select her, made another adjustment same as above but reduced opacity to 40%. Then for the boy, same thing, reduced opacity to 20%, and finally for Mom and the other girl, same thing and reduced opacity to 15%

And finally using (free) Picasa retouch tool, I removed some dirt spots from the girl's red sweater, took out the reflections on Mom's glasses and removed the remnant of the ribbon in the top right.

WHEW! That took longer to explain than to do. :)
Point is, you have the tools to do all this. Just don't get frustrated. I've only been playing with Elements for a couple of months. Have fun!