A residence requirement is simply a court order that requires a person to reside at a specified place for the period of the order. "Reside" is generally interpreted to mean "live and sleep at" - not to remain there 24 hours per day.
The domestic abuse programme you refer to is an approved Home Office programme which aims to educate perpetrators of domestic violence about the effects such actions can have (which, believe it or not, they may not have thought about) and also aims to provide education which will encourage a change of behaviour.
Both of these are usually imposed as requirements of either a Community penalty or a Suspended prison sentence. If they are breached when imposed as part of a Community penalty, the sentence can be revoked and a different sentence imposed. If breached in the case of a suspended prison sentence, the custodial sentence can be activated.