I have studied some Tai Chi these past (lessee now) 11 years or so, and I do not mean to be one of those guys who opens all messages with the I been there and done that etc., etc., etc.. I don't think or feel that egocentric.
However, I have done some push hands work and perhaps have just bumped past beginner in Yang Family Tai Chi (my Tai Chi nickname is "Limping Ox") and can offer the followings:
It would seem to me that an External MArtial Art is one which (like kickboxing perhaps) just teaches catalougs of techniques. An internal art would direct its primary attention to a particular type or group of body and mind development or sensitivities.
Experientially, when I practice Uechi Form, I sweat from a fairly deep core of my body, with Tai Chi, it's as though I have swallowed a halpina pepper. A bit deeper, but not distantly so.
AS to push hands, I (there's that word again) have been working a bit with four corners, single hand and freestyle.
The four forces, if it is helpful, practiced in four corners are: Wardoff (Peng) Rollback (neutralize)(Lu), Press (Ji) and Push (An).
There are eight forces altogether, but I only recall five at the moment.
I beleive proper push hands practice is both helpful and difficult for a Uechi Practioner. It is both good for your centering and confusing as you learn new methods of shifting, much like learning a new language or dance.
If I can be helpful I will try to do so.