what does mr bennets allowing lydia to go to brighton establish about his character?

I think the answer is two fold here. First he would live to get rid of another daughter to a man of wealth. This was a chance for Lydia to hook up with somebody like Wickham.

Secondly Wickham considers Lydia a silly girl who might as well make a spectacle of herself somewhere else rather than inconvenience him. Certainly this doesn't cast Mr. Bennet as father of the year! When it comes to his daughters, he has his own agenda.