The situation you're describing does not make sense, in-character, and I don't believe a reasonable DM would allow that to happen. Why would you pour so much energy and effort into inspiring someone of whom you are jealous?
The jealousy is a character trait. I'm not suggesting that I, the player, am jealous of anything.
The rules give the mechanics for what happens when you take certain actions, but that doesn't mean anything can happen just because you've twisted the rules to an end they were obviously never intended. If you try to give that Inspiration to Peta, then the DM takes it away because you are no longer playing your Flaw.
I think you're confusing the rules for earning Inspiration with the rules for spending them.
From pp 35-36 of the Basic PDF:
Your DM can choose to give you inspiration for a variety of reasons. Typically, DMs award it when you play out your personality traits, give in to the drawbacks presented by a flaw or bond, and otherwise portray your character in a compelling way. Your DM will tell you how you can earn inspiration in the game. . . .
If you have inspiration, you can expend it when you make an attack roll, saving throw, or ability check. . . .
Additionally, if you have inspiration, you can reward another player for good roleplaying, clever thinking, or simply doing something exciting in the game. When another player character does something that really contributes to the story in a fun and interesting way, you can give up your inspiration to give that character inspiration.
There is no requirement that the die roll that benefits from the Inspiration be related to playing out personality traits. There is no intention, stated or implied, to the contrary.
Likewise, if I want to give my Inspiration to another player, I don't have to have any regard to my own PC's personality traits in doing so. No such requirement is stated or implied.