Yes of course you would like some help and interest. You are a new mother and we all remember what that was like! I am a grandmother of 4 grandchildren and mother to 3 daughters. I have always been involved with the babies and am on rota's for care/school pickup'occasional sleepovers etc. This is, I've realised, because i am the most trusted, closest female my daughters know. They do not know their mothers in law enough to say what they'd like or not like for their children or that they'd understand their worries. Your mother in law is aware you are not their daughter and may think anything may be considered interfering or thinking they know better.
Mothers of sons are terrified of doing something wrong, not saying the right thing, looking overbearing, interfering, etc etc.
Just ask if mother in law would like to go a walk with you and baby. Let her push pram. You are doing nothing wrong this is just mother in law being cautious. Not replying to photo's is probably due to her not knowing how. Many people are not social media competent. My middle daughters mother in law didn't even reply to my daughter messaging she had Covid!
Try a very slow approach and if there's still no response you've made an attempt.
Your husband will not understand or even register there's anything amiss.
Very best wishes.