(((((Dublin)))))
You aren't betraying their memories honest! (even if you feel that you are.)
You loved both of them very much, and they must have had a wonderful life with you (you're a wonderful person, thats why). You made a hard decision in the end, which was for their own benefit because you didn't want them to suffer.
That makes you a wonderful mom.
All of the pets in my life have had to be put down for various reasons, all because they got so sick that they were suffering. It was the hardest decision any one person in my family have made, and I'm still sad when I think about them. I'm glad that they are in a better place though, where they don't suffer.
When my family's last cat got put down many years ago, and when we got a new cat 2 December's ago, I thought they (my parents) were trying to replace our old cat. They weren't, this new cat needed a home desperately and we had enough love/time for her and space. I'm never going to forget our other animals, but I do love our new ones as well.
I hope that this new puppy brings joy to your life, and that it finds a place in your heart that doesn't replace what you felt for your other pets, but takes away some of the lonely feeling that you're feeling.
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