DO NOT shake the eggs or kill any geese. Without the proper permits you will be breaking migratory (federal) game bird laws and will get your tit in a ringer real quick. The key to getting rid of geese is consistency. In February and March they are establishing nesting areas, so this is the most critical time to start harassing them. You need to chase them off the property every time you see them, preferably AWAY from the water... into some corner, hardscape, fence, treeline, whatever if they don't fly... Anything that scares the living buhjesus out of them. If they go into the water, you need to get them out. A Labrador, or a remote controlled boat, or an empty bleach bottle half-full of rocks tossed behind them on a rope... You need to get them out of the water. If not, they just wait for you to leave and come back out, and you've basically accomplished nothing. Scare them away, persistently and consistently. If you don't do it before they go to nest, you're basically screwed until after the young are born and fledged. Then you need to start the process all over.
As far as the kids go, someone needs to decide to be a parent instead of a friend... and tell them the truth about the geese and goslings. Doing it under the cover of darkness or when they aren't home isn't going to solve the problem. Geese need 3 things... Food, Water, and Space. If you aren't completely getting rid of one of those elements, which in most cases isn't possible, the only other solution is harassment. You can get kill permits or egg shaking permits, but the State generally won't issue them unless you've tried these other tactics.
