Check cables under handbrake first...I assume their both intact. Do not just randomly tighten them unless you can pull out the cables...they should just be lightly snug.
Then you actually go to work on trying things that might actually help.
First, when moving at 20 mph, pull up on the handles...this will clean the brakes, and might be why they're not holding.
Failing that, then try adjusting them...just remove one wheel bolt to do this adjustment...many diys around for that.
Failing that, you remove rotor and look underneath at handbrake mechanism. Worst is usually just that you maybe broke a spring or something.
Odds are that it just needs to be adjusted though...kind of a pitb but not difficult, per se.