Even on the 'good' modem I occasionally get drops in the RU connection (ie. I get signed out and also lose remote connection). On the good modem this doesn't affect anything else; I don't lose the ability to navigate.
What I am currently thinking is something like this: perhaps my internet is not very stable. Let's say I get microbreaks in the signal. For some reason, this computer deals with them OK when connected via some modems, and with others it gets confused/blocked somehow.
Yes, absolutely. Note that you may not notice such small breaks when you use a web browser because a web browser essentially just downloads a web page onto your computer and then you view this page offline (perhaps this explanation is simplified a bit but still applies to modern browsers).
Things are different with remote controls though. They need a relatively stable connection to "stream" remote image and keep the connection alive. The fact that some competitor products may seem "more stable" doesn't mean they are. It only means that they found a way to trick you into believing that what you are seeing on your screen is a real time image (whereas there might be a complex algorithm in effect to "smooth out" little network disturbances).