KLM is actually quite good in economy (with kids) with decent service, food, and entertainment.

I suggest paying for the seats and getting seats in the last row of Economy comfort for the adults and put the kids behind it in preferred seats for the overnight flights if on the 777W with a row of 4 middle section. One the 747 economy comfort is only 3 across so not an option. Looking at the total expense of the trips it is a small premium to pay for increased comfort.

Schiphol is an easy airport to navigate and Amsterdam is a fantastic place for a stopover and very kid friendly.