Really fresh eggs are a total pain. Its something to do with the lack of air pocket. I find that if you boil them, cool them, crack the shell and then leave in cold water that they peel a bit easier.
2 eggs a day? Wow, i probably have 2 eggs a fortnight. Maybe I should think about eating them more often. But yes, cooling them under the cold tap works a treat.
Two eggs a day sounds like an awful lot rosie29. Our doctors recomend not eating more than three a week, but then i know someone that eats five bananas a day!