Upvote:0
You seem to only consider two options: Use local pay-as-you-go SIMs with a cell phone or a mobile wi-fi router with one subscription while roaming. There is however no reason why you shouldn't be able to use a wi-fi router with different local subscriptions.
I know that it is risky to claim that something is not going to work, but there are several reasons why you won't (cheaply) be able to do what you are planning:
Pay-as-you-go subscriptions are in many European countries limitied to relatively small data packages.
Within the EEA, roaming surcharges have been prohibited since last summer, but there are exceptions. The whole-sale tariffs for data usage (what the network operators charge each other for their subscriber's data usage while roaming) are still quite steep. Therefore most (if not all) subscriptions with unlimited domestic data plans have some kind of limit or restrictions to roaming usage.
In many European countries, cellular coverage or network capacity is so poor, that you are not likely to reliably stream high quality video in most locations.