How does Brinker get Gene and Finny to attend the mock trail?
Gene and Finny have no choice in the matter of attending the trial. Brinker brings several people with him when he comes to Gene and Finny's room "after hours" and he essentially forces them to go along, saying "We're taking you out."
Brinker and his cohort "half-lifted" Gene and Finny "half-roughly" out of their room and steered them into the place of the trial.
Gene is, to some degree, trapped in inaction by his guilt for what happened to Finny and so is unable to stop Brinker. Finny seems somewhat amused at first and willing to go along. Importantly, however, Finny leaves the trial before it is completed and so his attendance at the mock trial is only temporary.