Dani, for a girl is short for Danica, or Danielle/Daniella. For a boy, I typically hear Danny being short for Daniel, but I'm sure there's at least one other name.
I was thinking for a few minutes about a middle name idea for you, and I don't know if typical "Marie" suits you, but I think Dani Marie sounds pretty. However, I don't like Danielle Marie, so it all depends on if you're going to name her just Dani, or if it's going to be a nickname. For a boy, I like Daniel James, or Danny Richard. Something like that.
My husband and I thought for months on a middle name for our baby that's on the way....and we're naming her Cambria [Cam-bree-ah], and we just thought with the first name being so unique, but not "out-there", Anne, would be the perfect match for the middle name. [It's also my middle name.] Maybe you can think of some names of people that inspire you, or just names/middle names of people you know, and you can pair them up.
I hope this helps you out!