Tl;dr: how do you deal with cockblockers?

I'll jump right in, I'm trying some red pill tactics on this girl, super fine 7/10. I'm in a GM, which annoys the shit out of me, with her (let's call her Carly), her friend (not relevant), and the beta buck, (Jim). He lacks so much confidence, it makes me pass the point of mad and into sad. He does that shit where he says something bad about himself to get a pity "that's not true" all the time.

So in this group message Carly said she just got out of a gynecologist visit, so the not relevant friend asks "what did it feel like to get things stuck up your vagina?" Me, purposely being playfully mean says "yeah, how was your weekend?" She gets "mad" calls me a jerk and asks for an apology I say no and white knight "friend" (Jim) comes in and demands I apologize. I say "fuck no" knowing what he is doing. He even brings it up in person with Carly around. I laugh and say no.

I text Carly that day (today).

Me: "I'm going to chipotle at 1. Come with me."

Carly: "Tell me you're sorry first"

Me: "when you get there I might"

"That's not good enough"

"Well text me if you're going or not by 12:00 because I got to make other plans"

Her (within one minute): "I'll go"

Me: "just you, see you then" I say this because Jim will ask her what she is doing.

Her: "okay"

I'm like holy shit this rp stuff works, I always thought it would, this is just the first time I've used it. Jim, of course, asks her what's going on. She said I'm having lunch with (me) alone. You're not invited. He asks me anyways and I say no and he asks for me to apologize again and again I say no. Then.. Fucking Jim follows us to lunch. Carly goes to my car after we get to chipotle and is laughing and asking what is he doing? He just doesn't care. Jim brings a book to read and tells us "I won't bother you, I'll just be other there!" Fucking cunt. I'm so mad but I don't show it. I play it cool and say OK. He sits down where he can see us and we can see him just a couple of tables away. Carly and I sit together and ironically Carly says "he is like our little hamster!". Jim keeps giving us looks like "yeah i know, I'm just over here" and Carly, after a couple of stares from him, just calls him over and says you're already here just sit with us, in a "you're a dumbass" way. We eat and we talk, I'm quiet most the time, talk to her a little and pretty much ignore him. I was more quiet than usual because I was trying to hold back anger. I say I have to go because I actually do and just leave them.

It's extra frustrating that Jim is getting his dick wet by this other girl he is not dating. How does he do it? What did I do wrong? What did I do right? Thoughts? Critiques? And the tldr above.