Well, depending on network speeds, a full node can handle dropping on and off the network quite regularly.

For LN, I'm not sure what the best solution would be. This article gives a good review of several common LN wallets and how well they worked with bad internet.

You might also want to look at how the LNURLPoS works, as it is capable of functioning without an internet connection, although it does this by using the phone's connection and not that of the PoS, so it might not be useful.

Maybe, depending on what prices you can get for data, rig up a battery powered LN node with mobile data that then uses a watchtower to account for times you lose service.

It you have someone that you trust enough, though, I would reccomend just storing it at their home.