Hi Mike.
Ok, there is plenty of information there. Based on what you are reporting, it sounds to me like the router is defective. I suggest getting another and swapping. That is probably the easiest and most cost-effective path because your time is worth more than this trouble. If that works and the original one is under warranty, return it for r/r and keep it as a spare, which you should have anyway.
Now, some comments/suggestions in the meantime...
Just for giggles.... reflash the current one with the latest firmware first (did it before? do it again anyway...) Do a factory reset. Reconfig and change the default user and password too. See it that fixes the dropped config problem.
As far as the firewall, I would enable it. You may also want to consider using a different browser (chrome?) for the config. I know I could have done a better job on the parser and gui on that device if I was blindfolded, especially the user-specified form stuff like LAN rules and VPN password. Their parser is braindamaged. The hardware seems pretty good though, but you must make sure it's well ventilated or it can croak from heat.
If you enable remote administration, you should be able to browse to your router using the dot 50 WAN ip. From what you say, you have been going to it when at the remote site when you use a PC on your dot 10 subnet (LAN) and you see the router has changed WAN address to DHCP and the LAN address to the 1 dot 1 default. That really indicates that the device is not storing the config in persisent memory. It would be interesting to see if it also reverted to the default user and password after you changed it. If it does... defective. If it doesn't.... something in the config is hosed and I would definitely reflash, factory reset and then reconfig again.
Just to give you an idea of how another setup is config'd, on mine, there is a cisco cable router feeding the RV ciscos (5 static which 3 are currently used). I have each router going into an HP managed giga switch. The subnet mains are attached there as well. Each device line power runs through an iBootbar which is fed from a big UPS. I also put a PC on one of the subnets. On the routers, I open & forward 3389 to the PC As a backup, I run VNC server on the PC. dot 254 forwards to the iBootbar.
One thing I have though is in my office there is another RV cisco. That has the VPN defined for each of the 3 subnets I use. The office is sub 0. Remotes are 1, 2 and 3. I didn't see you mention anything about a client or router. If you are using a softwre client, there may be an issue. You might want to consider router-to-router for your VPN.
Because of the way I have mine setup, I can remote access 2 ways, remote reboot hardware, cross subnets and more.
One thing I would recommend... for security purposes, put routers between your AT&T and the attached devices (controller, video, etc). Don't go right out of the AT&T into the device. IMHO, that is a lot of exposure.
I hope this somehow helps. Kieep us posted.
