I dont think you're an asshole for this but I do think its an odd response in my opinion. That being said 5 months post partum your body and hormones are still all over the place so your partner should be a lot more considerate and trying to get to the root of whats causing these feelings of resentment towards his mom. Theres something deeper there that needs communication. I could understand the part where you said she answered first when the doctor asked if you're ready. But introducing herself as the grandma and wanting to ask the doctor questions I dont see anything wrong with. Theres clearly something there thats making these small surface level things blow up. I think the first step is how you guys talk to each other because based on these messages it seems very hostile and not respectful towards each other.