When we went away in the van last year, we had no problem with internet to the extent that my 11 year old was able to tether his switch to my phone's hotspot and play Fortnite.
If you are in a metal skinned caravan, you might find you need an arial on top of the van for a decent signal, but if your caravan is fibreglass, it should be fine just on your phone. Again, though, it depends on your usage. An added benefit of a seperate router would be that it could be on a different network for occasions where the service from one is a bit shit. I would recommend EE and 3, if you are going that way.