None of that really matters if Mars is on the other side of sun from Earth. You'd need relay satellites to direct the signal around the sun, and even at the speed of light that's going to take tens of minutes, one way.

As the parents suggest, even at Earth-Moon distances, we need to completely rethink things.

I'm not a networking expert, but imo i think that with extreme delays, you would not want a real-time transport medium at all. The higher-level protocols would be built on top of a non-real time substrate. You would want to have so much forward error-correction that you could remove ACK completely (perhaps a higher level protocol could still be used to request retransmission in the rare case of failure, e.g. one could request a web page be resent via HTTP, but the hypothetical TCP replacement under that would have no concept of ACK).