Hi Angela!
Congratulations on your 1st Disney trip! All trips to Disney are magical but that very first trip is a little more memorable. Your family should be in for a real treat :-)
December is normally the time I take my family, and, also having young one's, we've went at all periods of the December month. The crowds between the times you're arriving should not be too bad, actually.
Many of the U.S. grade schools don't officially start their holiday break until around the 17th, so you may just beat that Christmas rush. We've went around the times you've indicated and found the lines to be moderately shorter as compared to, say, the 20th or after.
My recommendation is to beat the daily park rush (Disney, even on a slow day, can still be busy), get an early start at the Parks each day. If you're staying at a resort, use the morning Extra Magic Hours as much as possible, as only resort guests can get in, usually meaning smaller wait times on the rides until the gates open to the general public.
Late Extra Magic Hours have worked for us as well, but with young one's, they may not make it that long :-)
So, I think you're going to be in good shape Mom. Have fun!