Mark Cohen, I love the term and didn't come up with it, honesty forces me to footnote that to DivorceNet.com. At least that is where I encountered it. You can also say the mother/father of my children, if appropriate, rather than my ex-spouse...

And about lullabies: I sang the same several to them and they have picked, over the years, different favorites, so now Tim always gets Hush a bye (the Peter Paul & Mary version) and Wil always gets Castle of Dromore (the Clancy Brothers & Tommy Makem version). I hardly ever get to sing the one my father sang to me, Hush Little Baby, any more. Or The MLF Lullaby, another one of my faves.
One thing I do, though, is PLURALIZE the lyrics - so I sing hush a bye, don't you cry, go to sleepy little babieS, or Bring no ill wind to HINDER us, my helpless babeS and me... the original lyric is Bring no ill wind to HIM NOR us, my helpless BABE and me. And if I forget the plural one of them is sure to notice, sit up and say No, babEEZ! I also make a point of sitting on each child's bed to sing, now that they are in separate beds. The only discussion is who gets the first song, then I move to the other bed to sing the other song.

I read books to both at once, though, and there we have to decide on who's bed to read and then the other gets ferried over to his own bed.

About identical v. fraternal: you will probably be able to tell on the ultrasound what is shared, mine had separate placentas and separate sacs and were thus extremely likely to be fraternal, then they came out looking exactly alike but with different blood types, so we know they are fraternal. Also, whether twins run in your family or not will affect the probabilities of having fraternal v. identical twins. And I agree that it is important to know.
FFTKAT: Did you know that twins can be HALF-identical? Identical on the mother's side but not the father's? Can happen if the egg splits before fertilization. Rare but not unheard of.