Is ghusl obligatory for one who fondled his wife and she refused to perform Umrah until he kissed her, then he passed his organ over her vagina without penetration?

It is permissible for the husband to derive pleasure from between his wife's buttocks without penetration. Kissing the wife's anus is not indicated as being forbidden, but it is something that souls naturally recoil from. If these acts occur before entering the state of Ihram for Umrah, then the Umrah is valid. However, if intercourse occurs after entering Ihram, the Umrah is invalidated, and a camel sacrifice (badanah) and a repeat performance of Umrah become obligatory. If it is merely deriving pleasure from between the buttocks without penetration or ejaculation, it is a sin that does not invalidate the Umrah, but it necessitates the sacrifice of a sheep.