Not positive that this is how things work, because I didn't play this demo for all that long, but it would be nice if the pink moon didn't time skip to morning and end immediately after being caught and engaging in plapping activities, especially since it wasn't until the very end of my testing that I actually got one.
It's not a demo. But the pink moon happens every 14 in-game days, it happens exactly when there is a Full Moon. You can tell what type of moon it is by looking at the clock in the top right of your screen. You can also activate the pink moon by pressing the 'big red button' at the top of the campsite.
As for removing the capture mechanics, naw dawg. That's what makes pink moon difficult. The girls are thirsty.