Personal-level Tailscale is free for up to 3 users. So your immediate family is covered even on trips.

You could create an account with any one of their identity providers (or roll your own OIDC, it's possible) and just have it not have a linked credit card. The account you use to authenticate Tailscale doesn't have to be the Apple account that you use to log into the hardware device itself - my wife's laptop, phone, and iPads are logged in under my Tailscale account but separate Apple/iCloud accounts (we have family sharing for our apps, etc., but the TS is usually going to be up to me, so I haven't created another account for her). Free gets you 100 devices, so we're nowhere close to running out of those.