Are the leaves thick or thin? Do you know if it flowers? It looks like Ice Plant to me (sorry I don't know the scientific name). But I really could be wrong.

for kid play areas grass is your best option. looks from the photos that the grass failed in areas where there were likely tree roots, meaning the grass was not getting enough water (tree roots got it instead). you have quite a list of trees you want to plant, make sure you give them sufficient room, cramming a bunch together is a waste--and keep in mind they will affect the grass growth eventually with their shade and their root systems.

Go roaming around local parks and streams look near the crown of the trees there usually plenty moss in damp places. You can also look for moss in sunny spots then use those for sunny areas of your yard. Once you find moss you like look up "moss milkshake" and make it.

Thanks GG.... C_P.. You should see my yard. There's a moss that is very fine ..velvet-like, that has captured 25% of it. I live on the edge of a marsh. I personally like the moss. (kinda have to like it - or spend big $$ fighting nature) House is in the trees.. the other 'moss' is out in the pasture. I thought it must be an evergreen, but then GG says; "(although some mosses are remarkably drought tolerant!!)" ...so maybe, because it's mostly dry up front. Thanks again. Jim