As a total dog lover, I can understand your pain. Although it's not the same as losing a human family member, it is extremely painful nonetheless.
I remember in 2001 we lost my mother's dog (which I'd bought for her)--Ubu. My mother didn't cry at my grandfather's funeral, but I could hear the tears in her voice when she told me she had to put Ubu to sleep. I worked two hours away from my mother's city, but I told my boss I was taking the rest of the day off, loaded up my own dog in the car and headed to my home town to spend the day with my mom and grandmother.
Yes, losing a furry family member is nothing to minimize, and it's okay to be very sad.
