What do you mean you have paid for a 10 TV Roku plan? Roku themselves do not charge or offer any "plan". As far as your FUBO subscription, I see a Pro plan that says it includes "unlimited screens" but then says 10 at home. So I'm assuming that is the plan you have.
When you added the second router, did you put it in Bridge or Access Point mode? If not, devices connected to one router will appear to be on a different network than the devices connected to the other router. That might be tripping up your FUBO subscription, as it is thinking your devices are not on the same network. Although that seems odd since they are stating "unlimited screens". And they do say that you can have 10 screens at once on your home network. So my guess is your dual routers is confusing your FUBO account into thinking they are on two different networks.
If you put the second router in Access Point mode, then every device on the network gets an IP address in the same range and there's no confusion between the two network segments.
Rereading your post, it appears you might be using two different Internet connections (the hotspot providing one and your primary router on another). According to the FUBO web site, this should still permit two TVs on the separate networks to both stream at the same time. But I still feel this is what's causing the issue with your connections. My recommendation would be to run an Ethernet cable from your primary router to a location that would permit adding the second router as an Access Point as I mentioned above and use that to extend your WiFi to the less covered area. I have three separate access points in my home for this specific reason.
Dan
Roku Community Streaming Expert
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