A hawk scooping up my baby is my biggest fear!
I never let him outside alone for this very reason and he is always on his leash for walks and potty. I am so paranoid when I take him out to go potty that I am constantly looking up in the sky to make sure there aren't any around. My neighbors must think I hear voices or I am running from the law or something
! LOL. If I see a hawk anywhere around I pick him up immediately. I have heard so many stories of this happening to others that I am not taking any chances.
I just ordered one of those umbrella leash things (see pic below) to use in the spring/summer when there seems to be more Hawks around (and for rain too). I figured it would protect him and act like a shield LOL. I can hear my neighbors now..."oh look at poor Zeus now his crazy mom thinks its raining even when the suns out" Oh Well...it'll give them something to talk about!
I've also read that people put up those plastic owls or animated (motion sensing) owls to keep other hunting birds and pests away, but I'm not sure if they work!
As far as backyard play time the only I can think of is buying one of those Gazebo things and putting some fencing around the sides so they can play outside while remaining covered and safe. We got a cool one for our deck at Target last year at the end of June for 75% off so you may wanna wait for a month or two for the price to drop.
Good luck