So, if I read this correctly, the last time a reminder was given was two weeks prior to your parents going out of town, at which point your neighbor was supposed to watch the house and feed the dogs for... a few weeks?
If I understood that correctly (which I am not saying I did) then two weeks is easily enough time for a person to forget a simple promise to house sit and watch some dogs. Yeah, the house and the dogs mean a lot to you, but try being in her shoes: would you really remember something, on your own, for two weeks? If there was no personal benefit to you to remember (example of a personal benefit: you got paid for it), chances are good you would forget. A hundred other things could have happened to your neighbor during that two week period that "I just forgot" is a completely acceptable excuse.
If something is important to you (the dogs), then it is YOUR responsibility to make sure everything is set to go before you go. It would have been as easy as a phone call a week prior, "Hey Neighbor, just calling to verify that you'd be able to watch the dogs while we are gone. You still can? Ok, cool, thank you SO much! We'll call in a few days again just to remind you. Thanks again!"
Takes two seconds to remind someone, and more than anything it is polite. Remember, SHE is doing YOU the favor here. No benefit on her part to do something charitable, even if y'all are friends.
I'm going to guess you are fairly young, so use this as an opportunity to learn a valuable life lesson:
Being an adult means taking responsibility. Ultimately, you are the only one responsible for whatever happens to you.
Your neighbor is responsible for her life, just like you and your family are responsible for your lives. Your dogs are part of your life, not hers. She's not being a child by forgetting, she's just being human. The "responsible" thing would have been to remind her.
Not every lesson in life will be easy. In fact, most will probably come from tough situations; it's just the way things work. We (my family) have had pets die because of mistakes we've made, and hindsight is great for saying "would have/could have." So, don't think I haven't been on your page. It sucks, and I know because I've been through it. Everyone who's owned enough animals has been at that point one time or another.
The best thing you can do right now is learn from this experience, use it to become more adult yourself, because given the information you've posted, I do not see how any of this is your friend's fault.
[for the record: I have three dogs of my own and they are like family members to me, especially the two who are currently asleep in my bed. I understand where you are coming and have my complete sympathy and best wishes in that regard. I would hate to see anything happen to them, or any dog, so I definitely understand the sadness right now. But, life goes on, and losing a good friend over a stupid misunderstanding is much greater a loss, as least as far as I see it, than the death of an animal...]
(...wow...that was a really, really, really long post. And it wasn't even funny, I repeated myself a lot, and no one will ever read it. I can't wait to get off this medication that won't let me go to sleep. Seriously. Welcome to my life. I am embarrassed at myself now.)