Should I use Ditra for my slate floor with radiant heat and 2 layers of plywood?

Gypcrete is about 27% lighter than concrete (http://en.wikipedia.org/wiki/Gypsum_concrete). If it's not too late and you don't mind tearing up the second layer of plywood, the gypcrete will be a LOT more favorable in every way. Better for heat transfer. You can tile right over it.

That said, if you're already set on the path you're going, yes, I would use Ditra. You have to use something (a lateral anti crack membrane like Ditra, or hardieboard etc.) Ditra comes highly recommended as apposed to hardieboard. There are also Ditra alternatives that are the same basic thing (lateral anti-cracking underlayment.)

I recently completed pex installation on the main floor of my new house. I elected to use 14" I-joists on 16" spacing to carry the extra load of 1 ½" of lightweight concrete and ceramic tile on top of that.

If you can add floor joist reinforcement, I would just remove the plywood and pour lightweight concrete thick enought to cover your pex. Then tile over that.

Concrete actually has better heat transfer characteristics than Gypcrete and you don't need 3" of it. Gypcrete will also get soft if it gets wet so a leaking pipe could cause more problems. You also don't have the problem of your doorways being so much shorter. A 1 ½" loss of head height in a doorway is bad enough but 3" lower doorways and doorknobs is quite a lot.

Good Luck!