That is the order for the dances. The bride and groom dance first-if they want to.
There is no other order for dances. If there are special dances involving the couple and their parents, they just do them whenever. If you need them announced, tell your MC or DJ to do that. But guests are going to get restless and bored with too many "special" dances that they have to sit out of.
We did our first dance first, then my dad & I, my husband & his mom, then we had the bridal party dance, where the rest of the guests were invited to the dance floor 1/2 way through the song. Yes, I know, the bridal party dance is *not* popular among the ladies here, but it was the route we went!
Re: Order of the dances
There is no other order for dances. If there are special dances involving the couple and their parents, they just do them whenever. If you need them announced, tell your MC or DJ to do that. But guests are going to get restless and bored with too many "special" dances that they have to sit out of.