So we explain the situation and amend the Terms Of Protectorate (which currently doesn't mention trade except with us) so they can't trade with external polities without our involvement. We do Not use underhanded deals or strong arm tactics to backdoor the issue.We have WoG that a) such trade is possible, if unlikely b) if it happens, it'll be a veritable political shitstorm. I'd like to prevent that. Quartoks should understand if we explain them why it's a big deal and how their decisions can severely damage both ours and theirs political position in a Trust. They seem to be of a sensible type. Giving them a city for the sake of it is fine, we can gift them a third city if we need to, but having guaranties they ask our opinion before screwing up everything we'd done to establish their position is a good idea.
Upfront and honest is the best way to do this.