Router for Campground WiFi & Verizon Wireless??

A router will not address a weak WiFi or a weak Cellular signal so if that's what you hope to improve you will need some device the adds an external antenna to the roof, pole or ladder.
For campground WiFi you can do an inexpensive set for less than $100 but it won't help cellular. There are also cellular antenna/amp setups (Wilson Cradle is very popular) that will help with that side. They are very different signals and require different types of antenna for reception. If this helps, let us know what you would like to do to help with your signal reception.

I use a Pepwave BR-1 and two BoatANTs to do exactly what you want. Works great. Note that anything worth fooling with isn't going to be inexpensive.

If the campground WIFI sucks to begin with, you're not going to do anything to improve it by adding more devices to it.

WiFiRanger

Both our Cradlepoint and Pepwave routers will "failover" from WiFi to cell or vice versa as needed.

i believe their are several
i think 'cradle point' and asus have some models that do this

cradle point used to be mentioned on here quite a bit
how ever if you have a poor cellular signal for the phone or hot spot
you need either an eternal antenna or a cell phone booster aka "amplifier'

some of us use the wilson/WeBoost 'sleek' model
its an amplifying cradle with external antenna, place phone or hotspot in the cradle to increase cellular signal strength