If they live in luxury it can only be because they themselves had created the causes for that in their OWN past. If they have problems, ditto. Kamma is not transferable. The father’s (mis-)deed brought about the conditions in which THEIR OWN kamma vipaka could take hold – for better or for worse, for better AND for worse. Nothing unfair or ‘undeserved’ can happen at all.
Lal has explained it in pure Dhamma terms along with the workings.