Obviously you can't just hide all your feelings, but I now try not to be as frustrated about things that I can't help.
I used to think that I would be able to get an hour or two of work done when he was asleep,but the result was never good. I was stressed out after my third month of paternity leave. For the remaining months (we get 195 days to use as we please at 80% pay in Sweden) I just called down and learned to be happy with my day if we managed to
1. Walk the dog for at least one 1-2hr walk
2. Have some kind of social inreraction with grown-ups.
I now just sleep/relax whenever he's sleeping. Good days he sleeps a good 3hr mid day, and those days I try to get things done, but depending on how the night was sometimes I just do 3hr of relaxing and doing things that I know are good for me.
We get 195 days/parent at 80% pay (my union has however negotiated an extra 10% if I take most of those days consecutive during the first two years after the child was born).
Then we get an extra 45 days/parent with something like 100-150 SEK/day.
Until this year there was an extra bonus when the parental leave was shared equally between parents, so we got an extra 15k SEK (~$2k).
Feeling the weight of your little baby in your arms is fleeting so try to really experience it.
After he falls asleep in your lap you can put on some headphones and look at your phone.
From now on getting off the clock at your dayjob is just hour #1 of your night job.