Connecting through MUC is a breeze and a lot less confusing and chaotic compared to FRA. Non-Schengen flights arrive/depart on the third level; Schengen (domestic and EU) flights arrive/depart on the second and ground levels. Passport control is on the third level; once passed it, you just need to walk to your gate on the second or ground level. Free self-service coffee and newspapers can be found throughout the terminal building.

Luggage can be checked all the way through ATH where (technically) your sister and her family will clear customs if necessary (MUC-ATH leg is considered a domestic flight).

45-minute connection is rather short (for me personally) but since we're talking Germany here, they have to trust LH on this.