I'm trying to use AD2, and splitting the parts that are on the 1st track that have all MIDI parts onto the separate tracks with part names.  However, when I distribute the notes to their perspective tracks, the "Instrument" trx that have the combo MIDI/Keybd icon on them, which are presumably Instrument trx, they don't play their parts.

When I use AD2 I have one MIDI track and then either a bunch of separate audio tracks for individual drums or else one stereo track for the whole kit. The one single MIDI track contains all the playback information for all the drums. Are you saying you have (or desire) one MIDI track for each audio drum track?

Yep - One Midi track feeding multiple Audio tracks is the way to go and I would not advise using an instrument track for this - use split Midi/Audio