Year/make/model of RV would help. If the router requires AC power, you could get an inverter and connect it to the coach batteries by any number of methods. An inverter takes 12VDC power in and puts out 120VAC.
Mike. Comments are anecdotal or personal opinions, and worth what you paid for them.
2018 (2017 Sprinter Cab Chassis) Navion24V + 2016 Wrangler JKU (sold @ ????)
2016 Sunstar 26HE, V10, 3V, 6 Speed (sold @ 4600 miles)
2002 Roadtrek C190P (sold @ 315,000kms)