That theory has been laughed off already. Prigozhin’s plan was possibly 8 months in the making, there’s no way his family weren’t tucked away and safe. This whole event should be looked through the lens of something known as “razborki” - gangland warfare or mafia politics. Families are easy targets, Prigozhin is not that stupid.
A more plausible reason for the turnaround is that Prigozhin was counting on more Russian units around Moscow switiching sides and they didn’t, once he realised he didn’t stand a chance of steamrolling into Moscow with high numbers he backed off.