>> i believe the modem is just in bridge mode and the router currently in use
>> functions as dhcp

If it’s a modem only, there is no bridge mode - it just functions as a modem and hands out just one IP address - and you want that to be to the router. The router then does the DHCP. This is what you can’t just stick a switch on the modem first. You are kind of stuck, limited by the family limitation and your hardware limitation. I think u/danielvlee’s suggestion would be the least impactful if you could do it.

But I’d be willing to bet that whatever you do, the fam is going to blame every slowdown or issue on whatever you do. At my work, we put up some antennas for a project and the neighbor - a cable company’s satellite head end - started complaining to us whenever they had an issues - despite the fact that we did not transmit.