I can't see how dwarf mondo as an "edge" is going to help you. It seems like you would want a solid groundcover for the large shade area and its edge would be THE edge, without a need for any other plant. It's going to be impossible to keep dwarf mondo out of the lawn or out of whatever other groundcover you use.

Groundcover for a fairly large area seems to be one of the big "Chinese puzzles" of the landscape industry. Everybody hates an aggressive groundcover, but it takes one with some aggressiveness if it is going to hold up and spread without costing a fortune. It seems to be a general truth in life that cheap and easy solutions end up costing more in maintenance and bother over the long haul, whereas solutions that cost more up front, endure longer with fewer problems. A general truth about groundcover in particular is that if bordering neighbors are already using a certain type, it's best to use that same type, so long as it is adequately doing the job. If using a different type along common borders, it would be very difficult to keep them from mixing, and consequently looking somewhat messy.

The easiest solution, of course, is just a thick layer of mulch. But the disadvantages are that it requires periodic replenishment ($) and, as you've noticed, it doesn't hold up to hard "washing." Another is that it doesn't look near as good as an "upholstered" layer of green living "fabric." Take a look around your neighborhood/town and see what other people are using in similar circumstances, and evaluate its look and performance according to your needs. That's probably the best place to start.

Since you've fairly recently cleared the area of weeds and poison ivy, there is one advantage to keeping the area clear or just mulch only for one season ... because you can easily see, and eradicate with herbicide or digging, any weeds that return from roots or seeds, buying time for planning.

Keep walking through periodically and pick up the trash. I do that each early spring. Then try creeping red fescue or that ecograss.

I love vinca for a ground cover. no difficulty growing. is evergreen and spreads nicely without beig aggresive also helps with erosion

I know some people hate V. minor, but at least it doesn't climb and is open enough to allow bulbs to grow. I wish my prior owners had stuck to it instead of using it AND ivy AND euonymus. Pachysandra is also a very elegant ground cover, but is my denser. I'm not sure how they would be to play in though. Grass would probably be best for that.

A lot of this is going to be location specific. Without knowing where you are, most people are going to assume you are in a similar climate to where they live. My version of that is, you either weed or you mow. There isn't a ground cover known to man or nature that will stop the really nasty, woody weeds that you just cleared out of there. A lawnmower will. Alternatively, you can call local tree guys and see if you can get on a list to have them dump their chippings there.

I wouldn't worry about the erosion. Partly because I can't see it, and partly because I do see trees. Trees have roots. Roots stop erosion.

You all are wonderful. Thank you for the ideas! @Beth - I LOVE the first picture you posted! That would be so fabulous for the kids with a mix of big rocks, mulch, and grass. And the idea to add a more defined border is really smart. Thanks again for the examples! I just couldn't seem to find what I was looking for online.

We went out and picked out some more glass today and it just reinforced that some areas need some thick mulch or it's going to be glass city when the kids play out there.

We're in Virginia, which I should have mentioned. The dwarf mondo grass border was intended to just be a marker between the regular lawn and where I was going to plant eco-grass (which you don't need to mow). I don't love it, but they were so exhausting to plant in such awful soil that they're staying for now, ha ha.

Hi Cate, I'm in Prince William County, VA. The poison ivy is inescapable here - it keeps reappearing because birds love the seeds and deposit them freely. You just need to be vigilant. I would place a half dozen large pavers (slate or bluestone) around the playhouse to make a patio for the kids. Use large ones so they can be swept/blown clean. The mulch will need to be replenished twice a year (it breaks down quickly in our climate due to summer rainfall) so I'd keep the mulched area to a minimum.