Serve your goals first - the company has never and will never put your needs first, that is on you.
From my experience - the standards of 2 weeks versus a month notice tend to be hourly versus salaried position standards. So, if you are salaried, then a month may be a more standard notice.
I agree with pbkmaine - though it sounds like maybe your wife is not working over the summer so childcare is covered?
Working through the holidays would be off the table for me. The goal is spending time with your kid, keep that foremost (and any other goal) in mind when negotiating this work transition.
Congratulations! You will soon be free and all this will be a speck in your rear view mirror. Don't spend a lot of time fretting about this, your boss and you will quickly forget all this once you leave!