The following sentence is from this article on NHK Web特集
My attempt at translation:
When one tries to count it, they took care that the time shared with the son is very limited.
I'm pretty sure that 数えてみたら here basically means what I wrote above, meaning something along the lines of
If one tries to measure the amount of time...
But since it sounds very cumbersome in my translation, I wanted to ask for confirmation.