When replacing the bulbs in my three vaulted ceiling rotating can lights the units came out of the ceiling when I removed the bulbs... Two I was able to push back into place... no problem; the third won't go back in the hole and appears to have come apart from the ring... I'm using an extension pole with a suction cup on the end... The fixtures aren't accessible by ladder and I rather not have to get a lift of scaffold... Is there any possible way to snap the parts back together by pushing up from the bottom?

I doubt it, I see the only method of re-installing any parts is to get close up access to the fixture.