Interesting analysis. I'll admit to a couple "aww, cute" reactions to House and Rachel's interactions in s7, but overall, I think you're spot on: House saw his spending time with Rachel as an inevitability because of his relationship with Cuddy, so any effort he made was to stay in her good graces, not to actually foster any sort of bond with Rachel. He tried, but for the wrong reasons or in the wrong way.
I do think that stems from a fear of losing Cuddy/his addiction, either because she would wise up and boot him out, or because she'd be incapable of balancing her attentions between the two. Rachel was a roadblock, in House's eyes, from minute one; the look on his face in that shop, when he finds out Cuddy is adopting, says it all and his quietly backing out of the hospital room, when she tells him about the adoption plans a few episodes later, reinforces it. Cue the misery, pranks and overall madness that followed as House acted out his nuclear-level feelings of sibling rivalry and abandonment, and Cuddy's less than mature responses in kind.
Contrasting that with House's support- or at the very least acceptance- and involvement Cuddy's attempts to get pregnant in s2, when she wasn't labeled as this addictive romantic force in his life, makes it even clearer, IMO. At that point, he didn't see himself as part of the equation in her personal life, so her choice was one he could be involved in on the periphery without any fear or without anything to lose. Once those personal feelings started cropping up (yay season 4!) it was a much different ballgame.
But, as you said, Pete has none of that baggage. Rachel has always been a part of Cuddy's life, as he knows it. Coupled with being less jaded and less destructive than House, Pete knows that Rachel isn't something standing in the way, she's a part of the equation of whatever relationship he and Cuddy will choose to have.
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I do think that stems from a fear of losing Cuddy/his addiction, either because she would wise up and boot him out, or because she'd be incapable of balancing her attentions between the two. Rachel was a roadblock, in House's eyes, from minute one; the look on his face in that shop, when he finds out Cuddy is adopting, says it all and his quietly backing out of the hospital room, when she tells him about the adoption plans a few episodes later, reinforces it. Cue the misery, pranks and overall madness that followed as House acted out his nuclear-level feelings of sibling rivalry and abandonment, and Cuddy's less than mature responses in kind.
Contrasting that with House's support- or at the very least acceptance- and involvement Cuddy's attempts to get pregnant in s2, when she wasn't labeled as this addictive romantic force in his life, makes it even clearer, IMO. At that point, he didn't see himself as part of the equation in her personal life, so her choice was one he could be involved in on the periphery without any fear or without anything to lose. Once those personal feelings started cropping up (yay season 4!) it was a much different ballgame.
But, as you said, Pete has none of that baggage. Rachel has always been a part of Cuddy's life, as he knows it. Coupled with being less jaded and less destructive than House, Pete knows that Rachel isn't something standing in the way, she's a part of the equation of whatever relationship he and Cuddy will choose to have.