So for starters, look into replacing the U-brake with a V-type brake. Cost shouldn't be an issue; Shimano and other V-brake designs are available for about $25 a set. And of course, they should fit right onto the frame on the same pegs used by the U-brake. For additional stopping power, you can add a leverage-enhancing device such as a "brake booster," a wheel-like gadget through which you thread the brake cable. These are usually about $18.
You can also use different pads. Several companies make "extreme use" pads that are softer and apply more friction because they grip better. Shimano calls theirs "severe condition" pads and sells them for $15.
The last choice, if you really like the bike, is to upgrade to new wheels and disc brakes. That can cost about $500 when all is said and done, but disc brakes are great. I have a set of Hayes disc brakes on my Marin mountain bike and really like them. Good control, excellent stopping power in wet or dry conditions, and easy to take on and off.