As far as we know (there are a quite a few fibs being kicked around with these films) originally the main motivation for Anakin's fall was a growing distrust and loss of faith in the Jedi (helped along by Palpatine of course) but the Padme dying dream angle was wiggled into view in later cuts and some of the scenes of Anakin becoming more of a satellite of the Chancellor were dropped in favour of pushing that angle forward.

The main thing is Anakin is afraid of losing Padme and when you look into the murky vapours of the future things like, the details of loss, become blurred.

It may serve Palpatine's future plans to have both of the Skywalker twins appear to the remaining Jedi to be safe and to keep them away from Vader.

Vader will not live forever and the children will eventually be his replacements and Palpatine's insurance policy against the ambitions of his apprentice.

He could just tell him Padme is dead, she is certainly lost to him and maybe his dream was of a future time.

We could also see the bridge between the two trilogies in a decades passing sequence.

This would explain why the Death Star is seen under construction (years have passed) and Padme's eventual funeral.

Her niece (seen only in a few deleted scenes) could be a toddler Leia.

I liked the idea of Leia seeing Padme as a ghost (as in Curse Of The Cat People).

For all we know that power may come from the observer rather than the observed.

If Leia has latent Force abilities she could see her mother as a ghost but lose the knack as she got older and just put it down to a dream or a silent imaginary friend.