The only reason for bypassing the router was to see if the connection was good. If it was, then the router could have gone bad. It happens.
I am a bit uncertain of what you have though. It sounds like you are only using laptops and the wireless router is hard wired to one of them.
We need to find out what is causing the shutdowns and reboots. With a laptop, this can be a heat issue. Please note the time when the laptop hangs and/or when or does the reboot. Then follow this path:
Control Panel> Administrative Tools> Event Viewer> Click on System & Apps, one at a time on the left> look for Errors on the right> right click error> Properties> note description of error, Event# and Source.
There is a "copy" button below the up/down arrows. Click that, then go to any place that allows you to type (ie. notepad, wordpad, this board) and you can paste (use CTRL-V) the entire event details there. It makes for easy reporting of the event.
If you want to paste the Event here, you do not need to include the lines of code that follow the Description- but paste all else. You will be looking for Error that occurs at the time of the problem. Please ignore Warnings.
The Event Viewer has logs for everything that is occurring on the computer. It logs just 'Information' Events, it logs 'Warning' Events which can usually be ignored and it logs Errors which can be used to find the cause. Note Error that occur at the particular times mentioned. You will see multiple Errors. IF the ID# is the same, if the Source is the same and if the Description is the same, I only need one copy of each.