When I run my garbage disposal with any amount of water in the sink, it will pressurize the drain pipes and cause a leak from one of the connections. I have replaced all of the drain pipes and seals. Is there a way to keep the garbage disposal from pressurizing the pipes?

Garbage disposers do not really "pressurize" your drains. Spinning GD grinds the food and in some way helps to discharge water from its grinding chamber. Leaks are caused by faulty seals and / or connections. Make sure you have all washers installed, installed the right way up, and nuts are properly tied up. Double check your installation. Back to you. Milo