Obviously, it's pretty normal. I've had these kind of dreams from time to time, too. I think it perhaps is some kind of instinctive/protective thing in your subconscious?
I usually had nightmares about the kids when I was about to embark on something. For instance, before I made a trip to the US, I had a nightmare that the plane crashed into the ocean, and I was frantically trying to save my son and get out of the plane.
More recently, since being back in Chicago, I brushed up my resume and sent it out in response to a couple of ads. Then, I had nightmares that, while I was at work, there was an emergency at the day care centre and I couldn't "get" to it to help my boys. i.e. driving around in a panic, getting lost, stuck in traffic, etc.
These dreams can be unnerving when you first wake, but I think as mothers, we're just wired to protect our children.
Don't worry Liz, you're normal!