The biggest thing I've learned with a yeti. Fill it full of ice the day before a trip. Without putting anything in there. Thus is just to get it real nice and cold and get the insulation cold as well. You'll have a lot melt, that's ok. Drain all the water out. If there is still ice left, leave it. If all the ice is melted, or almost all the ice is melted put more ice in, doesn't take much now. The ice is just to keep it cold, not cool things down.
This will be when you get the most suction on the lid. The yeti's seal so well, the lid will actually be sectioned down from the ice melting (because ice has more volume than water). You can hold the bottom down and pull the lid up with your hands. The hassle free way is to unscrew the drain plug first. This will release the negative pressure, freeing the lid.