Two routers off one inteet line for two different networks

Ok here is my situation. My sisters family moved in with us and there kind of stubbo with the inteet. They want to use their router for their own network. The way I have it setup is we have our service provider modem going to our router witch creates our network and then their router is plugged into our router for their own network in their room. All they use it for is their PlayStation and phones. ( total waste if you ask me ) any time I do something with our router it effects theirs. Here is my question. Is it possible to go from the ISP modem to both routers so nether of them are connected to each other. I tried doing a switch from the modem and then to both routers but only one router gets inteet access. Iv heard of a network splitter. From one network cable/port to two cables/ports. Would this work or am I trying to do the impossible here? Any help or advice is appreciated

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