Current Rockville resident here
I've never been to Ellicot City nor do I care to (don't get me wrong, I'm sure it's a lovely place. Just have no reason to go there) so I really can't comment on what life is like in EC or HoCo.
I would recommend Rockville for most of your wants/needs. The only thing that would make me say EC is the fact that your wife is leaving the workforce. I'm guessing EC house prices are lower than Rocville if that is a factor.
But, Rockville for everything else
I'm a SAHM with 2 young girls (3 and 1) and I love raising my girls in this area. I live in a quiet neighborhood that has a little village center and parks. I love being able to walk to the village center and have store clerks know me and my kids. I love being able to walk to the parks to play.
Rockville also built their Town Center recently and it's close by. In the summer they have concerts and activities for the kids. They also have farmers' markets in the summer. Every Memorial Day they also have a big event (Hometown Happenings or something).
There's also plenty of shopping centers/malls around here. The Rio is a great shopping center with kid friendly stores and activities during the summer.
The Metro is also close by and it's wonderful to hop on (kids love riding the Metro!) to go down to DC to the museums and other attractions.
Since you said you will be working from home and your wife will be a SAHM, you most likely won't be affected too much by the traffic. My husband works 10 min. from our home and like I said, I'm a SAHM and wer're really not affected by the traffic.
If I were commuting on 270 during rush hour, my answer would probably be different! But my daughter's preschool starts at 9:30 and I don't go on 270, so it's not *too* bad. Plus, I schedule all my errands middle of the day and not during rush hour. It seems like you would also have similar flexibility. And we avoid 355 on weekends
In Rockville, you can creat a quiet, small town life for yourself but still have access to the offerings a big city has to offer. There is just so much for you and especially your kids to do down here!
So, yeah, Rockville is pretty great place to live. But it can be pricey, so that would be the big drawback against living here.