Reddit mentions of I'll Always Love You

I wouldn't specifically tell them she is going to be euthanized - to a 2yo and 3yo, that's equivalent to saying you're going to kill the dog. I would just say, as you mentioned, that she is sick and will die very soon and give them the chance to say goodbye. Then after she is euthanized you can just let them know that she died, without going into the specifics of how...just that when animals get old and sick, their bodies stop working and they are not alive anymore.

There have been a number of posts on the topic of explaining the death of a pet to young children which might give you some other helpful thoughts, such as this one, this one, and this one. One bit of advice that I've read several places is to avoid using the phrase "put to sleep", because you don't want the kids to associate sleep with death. You might also think about getting an age-appropriate book about the death of a pet to read with them, such as Goodbye Mousie or The Goodbye Book; two good ones about dogs specifically are The Forever Dog and I'll Always Love You. There's also a book by Mr. Rogers called When A Pet Dies which might help you answer any questions they have.

I'll Always Love You written and illustrated by Hans Wilhelm

I'll Always Love You killed me because my dog was my best friend when I was little.

Made me remember this book: http://www.amazon.com/gp/aw/d/0517572656/ref=redir_mdp_mobile/184-3472001-8566413

Reminds me of this here children's book that I used to have: I'll Always Love You

I'll always love you I recently reread it and was crying alone in my parent's basement.

I'll Always Love You

My mother read it to me and I'll read it to my kids.