Of course you are feeling sad that your grandaughter has taken a step back from you and a large step towards her other grandmother. You are only human and you obviously have a lot invested in this relationship. However, the more churlish you are about it, the more you will lose so grit your teeth, smile lots and reassure your grandaughter that it is lovely she has another person in her life that loves her so much.
Whilst I understand your angst, if you love her so much, you will want her to be happy. If two months with her other grandmother gives her such happiness, let her have that time without making her feel uncomfortable about it. I am sure if you can make the best of this situation, extend a hand of friendship to the other grandmother and are generous with your pleasure with the bond with her, you will ultimately reap the rewards of the love of your grandaughter.
Please ask your daughter not to try to influence your grandaughter, it won't end well.
I am sorry to hear you are widowed.. Maybe this is a wake up call that you need to find other interests too so that you are not reliant on somebody who will naturally move away from you as she grows up.