Not really clear why you want a router... do you have wired devices you need to connect, or are you just trying to have wifi in your RV?
If it's just wifi coverage, I solved that issue by setting my phone's hotspot to have the same SSID and password as my home wifi. I never turn it on at home as a hotspot so there's no contention. All of the kids devices and our smart TV connect automatically whether we are in the truck or the RV.
Where I think your request falls apart is having a router recognize multiple networks and expecting it to connect seamlessly. Range extenders and access points are more or less configured to look for a single SSID.
