OP, commuting by bike is nice, but don't get fixed just on that. There are plenty of ways how to stay fit and motivated, try to combine them with your passion for cycling. If it gets tough then look around, what other options are available? Perhaps you can arrange your life in a way that you don't need to bike/drive far to bring the kid to the daycare? Or maybe that you won't have to bring the child there often and spend more time together?

I have twin daughters, now they are two years old, and we commute, camp and travel by bike since they were five months old. At that time we got a used Chariot Cougar with hammocks and it's put to use practically daily.

I took the advantage of the local system and got six months of partly payed parental leave, so our mom could get back to work (she needed that badly by that moment). I used the trailer almost daily, this was the only way for me to put the kids to sleep outside on the fresh air. That was about 20-25 kilometres of riding like 6 times per week. Pretty good mileage for the situation.

Later I switched to the home officing so that we could move to a smaller city where my wife's institute is, we found a larger appartment for the same money we payed before, daycare is really close to our place, etc. Now I still need to go to the office once a week and get back home the next day. That is ~50 miles one way and I do it by bike. This and couple of late night training rides per week cover all my needs for cycling. Surprisingly I am less fixed on cycling now and two years ago I was totally obsessed with it. Probably because the major part of my commutes was done by train and a little was left for the bicycle.

I realize that not everybody can have such a freedom in how and where to work, but three years ago I could not imagine I would find all those options. Good luck and give all your support to your wife, she'll need it. If the first few months (it can be 2 or 18) seem to be harder than "promised", don't worry, that's normal.

PS. The problem with a coworker doesn't seem to be a real problem. It's a matter of explaining that guy once that you don't feel like discussing this topic with him.