Awwww Lyn, I'm so sorry. It's hard to lose a beloved family member and also very hard to see our parents so sad. We've gone through this a few times over the last couple of years as my Mom & Dad have one-by-one lost their sweet old dogs, and it is so hard. They have just one left and Dad is bringing her up with him to spend the summer with us again in a few weeks. At 17 now we know that Muffy's time is short & I'm worried about how my dad will take her loss, too. I'm so sorry for all of your loss.
Regarding adding a new member to the family, I sympathize b/c it takes me time to grieve, too. However, I wonder if you were to foster a dog for a little while if your Mom wouldn't fall in love with him or her.
Especially if he or she had the type of personality that your parents are usually drawn to. Do you think that that might work? In any case, your parents are blessed to have your love & support during this sad time.