I wouldn't cut contact with your parents (unless they're completely unapologetic about losing your dogs). However, I would use this as a learning opportunity to manage your expectations from now on. Like others have said, your parents have shown you that they won't listen to your explicit instructions, so, to put it bluntly, from now on don't expect them to.I'm truly feeling for you in this situation OP, and I agree with your husband that you won't be able to fully trust them in situation such as this again.
My wife and I have had our trust shaken in a somewhat similar fashion while on vacation for a week this year. We asked my wife's Mother and Brother to housesit for us and take care of our dogs. MIL just met a new guy and BIL is a college student. Our only two instructions were:
Both MIL and BIL are busy, work/go to school and have varying schedules. We didn't expect that they drop everything to come take care of our dogs, just that they stay the night with our dogs to keep an eye on them.
Right off the bat, we ran into problems. Since MIL was in a new relationship and BIL is a college student, both them would arrive at our house WAY late in the evening. Some days, they would feed the dogs at ~6 am and not return until midnight or later. Other times, we would get inconsistent answers as to who was staying the night that night ("MIL's coming staying tonight" then we'd hear "BIL's staying tonight") and we'd have to play phone tag until someone finally (begrudgingly) agreed to stay the night.
It got to be such a hassle and so inconsistent that we almost "fired" them and asked our friend (who lives out of town) to take over simply because we knew he was reliable and the whole situation was ruining our vacation. After a very stern discussion, both MIL and BIL apologized for their behavior and agreed to stick to a fixed schedule for the remaining few days until we got back.
Then, a couple of weeks after we got back, MIL told my wife that on a couple of the times she came to the house, she brought her new boyfriend with her. She purposely didn't tell us because we asked her not to bring anyone, and didn't want us to be upset. Of course, we were upset.
My wife and I both learned to manage our expectations of her family, and as such, we've made the decision to handle the next situation differently. If we decide to employ her family to house sit again, and that's a BIG if, we're going to be very clear what we expect from them. If they fail at those expectations again, that will be the last time we leave them in charge while we're gone. In your situation, with such a colossal failure, I would certainly never trust your parents to watch dogs again, but I wouldn't let it ruin your entire relationship either. In time, you might learn to forgive them, but I wouldn't ever forget it, and don't give them the benefit of the doubt for future decisions involving them.