Adhesive for PT lumber

Because PT is most often still quite wet when you purchase it I prefer a Polyurethane glue which cures faster with the presence of moisture. Gorilla glue is one of the most common polyurethane glues.

With that said, Home Depot and IIRC LeeValley sell a "Gate Kit" that includes 4 steel reinforced angle brackets that receive 2x4's for the frame of the gate. 2 of the brackets have HD hinges. This results in a gate that stays square and does not sag. About $30. If nothing else the kit saves you $30 worth of time and effort. I always use these kits when building gates now.

I've used Liquid Nails heavy construction adhesive on outdoor projects with good results.

Get a better wood (I used Spanish cedar) and make the gate a focal point. Brass hardware looks very nice on it.

I made 2 combination arbor-gates about 7 years ago from PT lumber. I used Titebond 2 for one of them and polyurethane on the other. (I believe it was Elmer's brand) Can't see any problem with either one after 7 years. This was with joint quality that was closer to "woodworking" than "carpentry". If I was building something with gaps to be filled I would use one of the construction adhesives that comes in a caulking tube.

Then there's mortise and tenon with offset bored holes with draw-pins. The way they use to build barn frames that have lasted a century or two.

After my limited experience with Gorilla glue, I think I'd stick with PL 400 (construction adhesive). The polyurethane glues get all foamy and aren't that strong, IMO.

As always, YMMV.

Those kits are just as handy as a bag of chips. I made a couple of gates, 3 years ago at my mom & dad's, and one of them is being slammed all the live long day. No sagging?the baked on finish is holding up well.