It’s crazy. My short stint working in child care I would always call the male parent first if I had their contacts, but it seems deeply ingrained in people to consider a mother “parent” and father “helper”.

Maybe they’d be more comfortable calling you if you called them every day “just to check up, to see how the kid is doing”, making it abundantly (and annoyingly) clear that you have nothing but time for your kid. And encourage your wife to respond “Have you called the primary contact?” whenever someone calls her.

I only have my own phone calendar, no shared alternatives unfortunately, but there is a multitude of options when you search for “family calendars”. Or create a personal calendar for your child with both of you having the password and colour code it for who is responsible for each entry.

Talk through how you want to deal with this in your family, but here are some suggestions:

Give daycare, pediatrics, classmates parents, and family and friends your contact info and instruct them to call you first hand for appointments, meetings or emergencies. Don’t ignore calls from babysitters, daycare or medical staff regardless of how important your current meeting is. You’re the primary contact.

A lot of them will still probably call your wife first no matter how hard you enforce this, so enforcing this will split the burden and responsibility.

Make sure you know your child’s SSN, birthday, allergies, sizes, current number of socks, favourite toys, and teachers and friends. Dress them for the weather they will be in throughout the day, and always pack extra because they will get wet or dirty or lose stuff.

Keep a family calendar where you can see appointments, and make sure to take a majority of those appointments if possible (plenty of responsibility will be pushed onto your wife regardless).

Add playmates and family members birthdays and other events to the calendar, and go shopping for gifts at least a few weeks before, without being prompted by anything other than the calendar. Wrap the gifts yourself or pay for wrapping at the store.

Let your wife know (or maybe add a checkbox to the calendar and check it off when the preparations are done) that it’s taken care of if it’s a shared task, but don’t bother her with it if it’s your specific job - that’s your responsibility and nothing she needs to keep in mind at all.

Keep count of diapers and socks and formula etc, and buy new (in the right size) without being prompted. You don’t need instructions for every little thing regarding your own child, you can take responsibility without being given it.