I thought the end of 1.07 was just for the sake of the cliffhanger (I heard some intimation of rumours that they did actually intend Peter's character to be a bit darker, until they saw the fan outcry during the hiatus after 1.07, but I generally avoid behind-the-scenes/TPTB stuff as much as possible, so I don't know or care how true that is). And yeah, I agree, the weighting of the show towards Neal's POV (and Neal's woobieness) makes a lot of people resent Peter. I am not one of those people. :-)

Though, actually, we see Peter's inner workings in his scenes with Elizabeth, including El's awareness of how emotionally invested Peter is.

*pets everyone*

Why couldn't (or wouldn't) he get a meeting with them both together?

Because he wants Neal to forget about Kate and focus on rehabilitating himself. Why would he take Neal there? That would just feed into Neal's overblown narrative of his life as a romantic tragedy.

Also, as you've pointed out elsewhere, Kate was (possibly) avoiding Neal for some or all of their recent past, and she's still keeping her distance, for whatever reason -- maybe Peter thought she wouldn't want to see him, or she vetoed Peter telling Neal they were meeting. Who knows?