Lay down some crushed stone and then some fine bark mulch.

She will probably still have to spray for killing weeds. They sprout everywhere, even in naked rocks. Get a mechanical tamper from the rental place, to firm up crushed stone or stonedust. Makes it more even, packs harder than anyone can by hand. Rental is not expensive.

Have you done any below ground digging stoppers in the plan? Some dogs, some breeds, just will keep trying to dig free. Laying chicken wire along the bottom edge of perimeter fence, about 6 inches down, then cover with your fill dirt, stones etc. Worked for our German Shepherds when I was a kid! They were determined escape artists. Could scale an 8ft fence straight up! Had to get those angle things so dogs fell back inside the fencing at the top. If she is well off, those large pavers, 18"-24" squares edging the inside fence bottom are a good stopper to digging. Heavy to move, even for the determined animals. They also make a nice path for dogs to jog on, without leaving ruts and mud. As you said, sand base is just too easy to dig, actually attracts insects to live in. Sand here in MI usually has fleas in it too.

I don't know if I would use mulch over dirt/stone, but maybe in parts of the big yard area it would work. Mulch does work at turning into dirt!!

Make doghouse location easy to clean. Perhaps handles on the doghouse for moving, lift up roof for cleaning inside. You would be AMAZED at the critters who move in under the doghouse. Rats are especially nasty but like having dog food and water readily available! Some dogs seem to just get used to the rats, don't even try to kill them. Little dogs could be too small of course. Anyway, easy lifting, the ability to check for critters, should be figured into the pen. Some shade in one area. Those tarps, black mesh screens work well for shade if no trees are inside. Tarps allow good wind flow, unlike staying in the doghouse.

We use bank run, a road gravel mix, sand/gravel/stones, some clay, to fill things. Drains well, will grow some grass, usually not muddy. Sets up firm, but a bit of cushion so not hard on joints and bones of animals running about on it.