That’s how I took it too.
I think he’s frustrated because he was just talking about how he thinks that his father was so happy that Yamato is at Aiko’s (implying that he’s glad to be rid of Yamato) that he even offered to pay food expenses to Aiko-san.
ちゃだめ is a casual form of てはいけない.
If it was me it was probably Japanese Colloquial abbreviations, if it was someone else there’s a good chance it was Quick Contraction Reference.
Starting with what you talked about, here's the gist of the group conversation
- They want to put up a poster in the cafe to get neighborhood kids to come to their Night Cafe event.
- They’ll start with a few kids around elementary school.
- They’re gonna take a small bit of money (probably 100 yen per person) to make sure that they don’t have to stop if a lot of kids come, and to make the kids not feel like they’re just taking without giving anything.
- Staff roles: Saki and Yamato are cooking (and Aiko, if she has time), Tina and Hanabi are talking to the kids.
Can’t help you with the ていく question. I practically never understand it when it’s not related to motion, and I usually feel like I can just pretend it isn’t there and the sentence is just fine.