Even though Ted gave Robin his lovely speech in the car about letting her go, he didn't really let her go. Naturally, because we're going to beat this Ted loves Robin nonsense into the damned ground now. So he sets about dealing with this by going overboard in planning their wedding, with big binders and an obsession with having a DJ. His overcompensation pisses Lily off and the two go head-to-head in a heated war over who gets to plan the wedding and if there should be a band or a DJ. Eventually, she realizes that Ted is still not entirely thrilled about this engagement. She takes him up on the roof and confesses her darkest secret (sometimes she wants to run away from her child) and he follows suit with his thoughts that Robin should be with him (can someone please slap him? Can it be us?). Then the twosome sulk for a bit before remembering they are adults (at least by age) and have to deal with their lives. Of course, this means they book some band that Lily almost had at her wedding, that band quits at the last minute and luckily he runs into Rachel Bilson and Ivy Dickens (for a second we thought we were watching the Gossip Girl finale again) on the subway, and Rachel recommends her roommate (you remember, the one with the yellow umbrella from a hundred seasons ago) who is a bass player in a band and conveniently available. So the answer to the age-old question here is Band, because if he'd gone with a DJ, all he'd end up with is stupid party favors instead of his future wife at the end of the night.
Post-engagement, Barney is still coping with the fact that he's no longer what you'd call single when Robin discovers he didn't ask her dad for permission. So in strides Ray Wise, who is living in New York, now a Parrothead and obsessed with Facebook. He gives Barney a ton of crap about marrying his daughter, mostly saying that he won't let his little girl (he remembered she's a girl!) be with a grown man who is blonde. Cue Barney with dyed black hair and a burning desire to do anything to win over Robin's dad -- well, anything except murder an adorable bunny in the middle of the city. But Robin gets all pissy when she finds out through Facebook that her dad has been living in good old NYC for eight months without telling her and got married to a girlfriend she never even met without inviting Robin to the wedding. She decides his permission isn't important (though we're not sure why it really was in the first place given her strained relationship with the man) and tells him he's not invited. But Barney brings them back together, and he apologizes (well, as much as he can) and they end up dancing at her wedding.
In another major subplot, Marvin is constipated, and when he poos, it looks like confetti. I don't get how 2 Broke Girls can make all the jokes in the world about anal sex but this show can't even talk about baby crap. That said, after watching Friends with Kids, I'm kind of glad we didn't have to see Jason Segel covered in shit. Why couldn't Segel have made Muppets 2 instead of sticking it out with this show another year?