We got a playset (Backyard Discovery Woodridge Elite) but upon building it we notice a considerable amount of sway at the tunnel/clubhouse connection while swinging on the far swing, closest to the ladder. There is a little movement on ladder side as well but not nearly as much.
The sway is less when swinging on the inside swing, but swinging on the outside makes it sound like the whole piece is going to break apart from the clubhouse. Any advice as to minimize this?
This problem is best remedied at the ground, and not at any particular structural connection (though they should all be checked for proper tightness, etc.). The last page of the installation manual directs you to install a pair of "rebar stakes" to deal with that. I can tell from here that those aren't going to do the job. They offer virtually no purchase on the soil.
Get yourself a proper screw-in anchor kit. Run them in at those locations (ends of the A-frame legs), then anchor them to the legs with the provided straps. Use only through-bolts with nylock nuts, and not the lag screws in this photo. Lags work loose over time when subjected to dynamic loads. Keep them up at least 2" on the leg board to prevent tearout.
Make sure that there's no play in the system when you're done. The legs should be held firmly to the ground. It might make sense to put down a footing of some sort, such as an embedded concrete pad or block of treated lumber, to prevent the leg from settling into the ground with movement.
A typical A-frame swing set has A-frames on both sides:
The A shape is very strong against forces caused while swinging, since the sides of the A can't change length or angle.
While your swingset does have a semblance of an A on the climbing side (marked in blue), it does not have the A on the clubhouse side. What it does have is a rectangular box (marked in red):
While the upper part of the rectangle appears covered and theoretically more stiff, the lower part is wide open. A rectangle under the kind of forces in swinging can become a parallelogram very easily:
I doubt the yellow-highlighted mini A is sufficient to prevent this.
I think you need to add another A on the clubhouse side:
Locking the swingset to the ground, as Isherwood's answer shows, is also important.
