Is your dad running Windows? Windows firewall is known to block icmp traffic, a problem that neither Tailscale nor any other p2p VPN can solve.
The other thing to check is if he was running another VPN on his machine at the same time. Running multiple VPNs at the same time (both Windows and Linux) requires extra fiddling to map the routing correctly to prevent their rules from overlapping/breaking each. https://tailscale.com/kb/1105/other-vpns
Anyway, tailscale still has more to go. Inviting someone to your tailnet doesn't seem to be the same as adding a machine yourself.
I am, among other things, a network engineer, and previously I shared my tailnet with my brother's windows machine by logging him into my account directly, and it worked flawlessly.
I want TS to win, but they've got product and engineering work to do if they're serious.