You can't exactly dislocate your coccyx. I suggest you look up sacroiliac joint
as it does cause pain in that area if there's a problem.
If that is the case, things will be loose due to having given birth. Some of us are naturally looser down there (I have some hypermobility and SI joint dysfunction as a result). It should get a little better but physical therapy will help a lot.
Here's a very quick test for you to try to see if this is what the problem is. Go lay on the floor with your legs together. Bring one leg up and put that ankle on your other knee. (makes a figure 4) Have someone push (or push it yourself) the knee of the bent leg towards the floor. If there is pain around your tailbone and butt - it's your SJ joint.
I do suggest you get it checked out, if it doesn't tighten back up properly you can end up with very painful arthritis there!
I already have arthritis, obviously, but keeping everything strong has helped a lot. Back in December of '06 I could not walk for around 18-19 days due to a very very bad flare up. You don't want something like that happening.
As for bruising the coccyx, been there done that. The pain tends to go away after a couple weeks. I've heard fracturing it (from a very hard fall) takes longer to heal, of course.