Wow Sunny, that's something I never thought about before. You're a good grandmother to even think about this, especially since she's only 4 months old. My granddaughter is 4 and I see how some issues my daughter has could potentially make a negative impression on her growth as a healthy individual. My daughter is a fantasic mother, absolutely the best, I'm proud of her...BUT, big BUT here...she is really not very good at parenting. What I mean is she is OCD about lots of things. Cleanliness, Un-timeliness, obsessing about what people think of her, etc. Germs...oh my God that is the worst for her (she's a nurse and sometimes when you know too much about medicine, it can be very bad for your health

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But back to your concern. I don't know what you can do about it. I'm wondering if you could make an appointment with a pediatrician. Just make an appointment and if you have to you can ask to have a meet n' greet appointment. They do that...you don't have to have a child to take with you...you could just be making an appointment (with the receptionist) to meet the doctor. When you go for the appointment you can explain why you are there. Ask them what would be a good way to handle it.
What I do with my granddaughter is this. I spend quite a bit of time with her because we live close by. I try to show her what NOT being compulsive about germs and cleanliness and un-timeliness is, but in a very reasonable way. I try to set an example with her, not to undermine her mother's authority, but to show her incidentally that there are other people who she can trust that love her that live differently. She's only 4 but I can tell that she is aware, little by little, that even though she loves her mom to pieces and respects her, she realizes the differences betweeen her mom and other people. She is aware that what her mother does isn't always right. I think that is because she feels comfortable and trust me. Her father, god bless him because he deals with this ALL the time, is also a great father, but he works and as you know the mother usually has the most influence on their children.
It's a tricky situation, but I think it's good that you are aware of it so you can sort of counter balance that problem in your own way, but without undermining your granddaughter's mothers position in her life. Good luck, Marie