Suppmom, I can understand that you feel strange about reading the letters. I guess it's similar to reading someone's diary after they've died. But, I agree with the people who've said that if your mom really never wanted anyone else to see them, she would have destroyed them. She probably wanted her children to find them.
But, do what you want to do when you feel ready to do it.
And, just explain to your sister that she caught you off guard by giving you the book in front of everyone. She'll get over it.
Finish each day and be done with it. You have done what you could. Some blunders and absurdities no doubt crept in; forget them as soon as you can. Tomorrow is a new day; begin it well and serenely and with too high a spirit to be enbered with your old nonsense. ~ Emerson