The Fraupow Wet Dry Bags keep things hygienically separated with this waterproof bag. It will contain leaks all the way home, and once you've unpacked it just throw it in with the washing to keep it clean.
With two separate zipped compartments, you can keep one pouch for dry items and one pouch for wet items, or use both for wet whatever suits your needs that day. The pouch has a loop with a popper so that you can hang it from the buggy or attach it to your changing bag so it's always on hand.