For me keeping chickens is about sustainable living. Killing any predator in your yard is NOT.
Remember they have been there before you. We human enroach on wildlife - try to live in peace with your wildlife.
EXCLUSION is the key word - almost any "pest animal" can be excluded.
In your case, you might want to add fencing (hardware cloth with 1/2inch to 1inch) that is too small for the squirrels to get through.
Also feeding the squirrels might do the trick to distract them. Squirrels are not big on eggs anyway - I work in wildlife rehab and although we offer eggs to squirrels, they hardly never eat it when giving other choices.
Exclusion also works for raccoon, foxes, etc - trying to live in harmony with the world around you also might make you feel better about yourself and your chickens
I would love to see the pics of the squirrels rolling the eggs though, thats hillarious !!