Weeds may be crud, but the pine needles make fine mulch.

Lawn won't do well under pines. Shade is far too dark. And roots of well-established pines thoroughly explore every nook and cranny of the soil.

Could try over-sized containers with ornamentals. Or rely on under-story plants that normally live with pines.

If you are going to have kids playing underneath I would go for woodchips and containers.

Sounds like wood chips is the way to go after all. What about weeds though? I yanked all of them out pretty thoroughly and there's already new ones sprouting all over already. Will the chips inhibit the weed growth in any way? If not, what's the best (non-chemical) approach to minimizing weed regrowth in this kind of sitaution?

Try salal (Gaultheria shallon), oceanspray (Holodiscus discolor), and sword ferns. They're tough, and grow natively under large conifers.

Other native understory shrubs for dry shade:
Evergreen huckleberries (Vaccinium ovatum)
Indian plums (Oemleria cerasiformis)
Snowberry (Symphocarpus albus)

Perennials, ferns and groundcovers:
Bracken ferns (aggressive and tough, could be perfect for you)
Bleeding hearts (Dicentra formosa) are pretty, but might be too fragile
Wood sorrel (Oxalis oregana) -- aggressive spreader, supposed to be tough, not sure how it would do with the kids.

Use the King County native plant guide to find more. Check the boxes for dry, and shade, and hit search.