All of the Brihaus marriage content requires you to complete all the introductory stuff so you can unlock the repeatable content, ie do Rina and Cassia's content to the point where you decide whether you want to be lovers or platonic with both. At that point Brienne should have no further requirements to marry her and the option should appear in her menu (at Brihaus only) to the right of the Brush Hair option. Marrying all three requires Brienne and requires you to be lovers with both Rina and Cassia. When you start the marriage sequence with Brienne you'll be given the option of getting three rings instead of one.
Rina's colosseum event requires you to do her repeatable Training content several times (four IIRC, with a one-week cooldown between each instance) and then the event will happen a week after the final training scene. It's unrelated to the plans for the Champ to participate in fighting there and accessed entirely from Rina's menu.