T.F.
I'm around water a lot and kept needing a new camera like every year. This Olympus point and shoot has lasted past the year mark! It's waterproof and shock proof and over 7 megapix. It's small and I keep it in my purse, diaper bag, or back pocket. The view screen doesn't flip up, but it is water proof. I love the underwater videos it takes. I can zoom in and out while videoing too.
The shutter delay is b/c it focuses when you push the shutter button. I was soooooo annoyed with that until I realized that most cameras do that and why. You'll have to get a real (bigger) camera to get away from that. Just hold the shutter part way down, it often beeps when ready, then you can push as soon as the front of her head is back toward you. THEN it'll be an instant pic. I do that when my kids are on the swing. I push it half way down the first time they are being cute right in front of me (close) then take the picture the NEXT time they swing toward me with a huge smile.