I'll skip that SIM issue, that has been brought up recently several times on here and I don't remember the answer since I don't use the 3G/4G version.
For the WiFi, highlight the network that your iPad wants to join and then tap forget this network...that should then force it to ignore the other network. In spite of what the manual says, I've had mine want to join the strongest network on occasion. Usually, howver, it does very well going back to the last network it was on when that is available.
You might try going to Settings > General > Reset > Reset network settings.
Power down the iPad.
Power down the router, even disconnect power to make sure it actually is down, wait a couple minutes and power the router back up. Let it stabilize and capture a new IP address, then power up the iPad. Got to Settings > WiFi and join a network, what you did before entering the name of the hidden network, etc.
Do some work and then sleep the iPad and see if it will now remember the network when it awakes.
In many cases, a power cycle of both the iDevice and router work to get the iDevices attention.
What I've done is just change the setting under wi-fi networks to -> Ask to Join Networks - Off.
So, once you've added your hidden network and any other network you use it will grab the closest one that is trusted (Entered). What's happening is that your hidden SSID isn't being picked up first and it's grabbing the first open network.
I'm not sure of the logistics when you are not near a trusted wi-fi if the iPad will continously hunt for the hidden SSID (Potential batter drain). I'd be interested to know though.
Well, I did part of that, Ralph.
I didn't do anything to the router as it is hidden away and a pain to get to, so I thought I'd try the easy bit first.
I could manualy get it to change networks from the one it always seemed to favour (which was, oddly, one I had never joined nor ever attempted to join!) but when startig the next time it had forgotten my own network agan. It listed it, but gave it the cold shoulder.
I did tell it to "foret this network", then powered down, left it for half an hour or so (I was otherwise engaged, the 30 minutes wasn't a deliberate dcision) and restarted - and it went striaght to my own network.
As for the battery drain looking for a trusted wifi point I shall check althogh, as this is my first and only iPad, I have no point of base reference. At least three places where I shall need to log on hide the SSID, me and the theatre where I work backstage - we can't have the punters playing on the internet during performances!.