My heartfelt sympathy goes out to ya'll. A pet in the right home is a member of the family, so mourning is both appropriate and necessary. I have had several dogs that I had to have put to sleep over the years and have unashamingly cried like a baby not only during the process, but for weeks afterwards with bouts of saddness and more crying for quite some period. Grieving is normal...let it out, cry with Joanne so she knows she is not alone in this grieving. Holding back may not be helping her and from my own experience it did not help me.
My prayers are with you.