“You'll have to excuse me” is a fixed phrase which doesn't mean what it appears to mean.
Phatic expressions like “excuse me” are used to make the social aspect of conversations more pleasant. These expressions are typically fossilized from earlier very formal usage, and often “eroded” — worn down to the point that their literal meaning has vanished. This causes no confusion, however, since it’s the use of the expression, not its meaning, which is important.
“Excuse me”, for instance, is not a demand, as its imperative form implies, but a request, worn down from something like “I ask that you excuse me for interrupting you.”
In your example, Papa is being extra polite; perhaps he feels that a simple “Excuse me” is a little too abrupt, so he extends the expression. His extension, however, does not mean “You are required to excuse me”. “You’ll have to” is understood as if it were an eroded version of something like “I regret that circumstances put you in the unpleasant position of having to excuse, &c.”