I would get the signal on your modem (at your place) checked, drop-outs shouldn't happen... When it drops out, do the lights on the modem change at all?
Might try a different modem, but if you are on 10 internet, you will not be able to have your modem bridged, so if you want to use your own router, make sure it gets swapped for another Motorola, if it gets swapped..
When using the router, your speeds are poor, when you connect directly to the modem, speeds are good, that usually indicates the router is bad - the change one thing at a time to find when it breaks troubleshooting method...
Are you using wireless to your routers? Or wired connection? It could be a wireless interference issue as well.
I would suspect failing modem though. Everything else can be tested while waiting for a service call
Yes, I am not employed and looking for IT work. Have passport, will travel.