I have found references for using a hAP ac2 as a travel router, but could someone update the instructions for a hAP ax2? I cannot seem to find the connect button for the wireless connection to the host wifi network.
Under wireless tables you have option “Scan”. Here you can select desired interface, click start and when you see AP to which you want to connect select it and click “Connect”, I think that’s what are you looking for.
I realize now that I had to use WinBox to configure it. I have been able to connect to my wireless network as a test. However, I cannot route from my laptop connected via Ethernet to the wwan connection.
Remove wifi port from bridge.
Add dhcp client to this port.
Route will come dynamically.
And otherwise, show your config, please.
That did the trick! I now can ping the internet and my LAN from clients on the hAP.
Last question: how do I use this with networks that have client portals (like Hilton hotels that require you to sign in on a web page)? Connect it to the network and then login from the browser on the laptop?
Bonus last question: For those of you using it as a travel router, how do you pack it for travel? Is there a little case that fits the bill? I prefer to protect this gear rather than let it get brutalized.
Should work. Testing is required. Get to it. 
You may have a local hotel from the same chain. Walk in and tell the counter clerk what you’re trying to do, making it clear that a sale hinges on the result of the test. If you do your testing in the lobby, under their supervision, and you don’t hang out for a long time, they shouldn’t hassle you about using their WiFi without paying. Go in the middle of the day when things are quiet and the network isn’t slammed.
You can’t guarantee that your travel destination uses the same WiFi hotspot setup, but once you get this working, you will at least know that your travel router can in principle work.
Is there a little case that fits the bill?
It should be a mere matter of product research to find a MOLLE pouch that fits. I have one here that I put a hAP ax Lite into the last time I went traveling, with its smaller front pocket holding its oddball 5V-only USB-C power brick. I’d recommend it to you by brand and model number except that a) the brick on the ax² is bigger, and b) the pouch was of generic manufacture, so I wouldn’t know how to point you at it anyway, and that’s assuming it’s even made any more.
MOLLE bags make great techie gear bags regardless. You buy one main bag to hold the laptop, tablet, etc.; then however many small pouches you need to hold accessories like this travel router of yours. Sure, the assembled result makes you look like a tacti-cool wannabe, but you can minimize that by going with the black and sand-colored ones instead of the camo and olive drab ones. Atop that, it’s a project to get the bag set up and working as you like, but the result is functional, durable, modular, and expandable. There’s a tremendous fund of experience that goes into the design of military gear, and we civvies get to benefit from the result of our spent tax dollars. 
One of the nice side benefits is that a bunch of separate pouches make it easier to remember where each piece of gear is. The mnemonic system I use is that the shorty USB cables and memory sticks are in the upper pouch on the strap, the Apple-specific accessories are in the abajo pouch (Spanish for “below”) and so forth. I need no mnemonic for the water bottle pouch I use to hold my longest lens, its function being obvious from its shape, nor for the MLC camera body pouch since its size and location make the contents obvious to one (i.e. me) who knows it’s there.
I prefer to protect this gear rather than let it get brutalized.
I should think the ax² would put up with quite a bit of punishment. Your biggest practical problems are going to be keeping crud out of all those vent holes and keeping things from jamming into the RJ45 pins to the point that they get mangled.
A Ziploc baggie might therefore suffice if placed in the middle of your clothes bundle.
Then something like this could come in handy: https://www.amazon.com/RJ45-Jack-Snap-Cover-Inside/dp/B001S52NX8
Couldn’t hurt.
For all tech gear in my laptop bag, I use Peak Design Tech bag.
This has worked for me, as I too use an AX2 as a travel router: