Is it permissible for my wife's mother to leave her home and come to us in Saudi Arabia to perform Umrah and reside with us, knowing that some relatives have stated that she must remain in her home for three months for mourning, and that she has two other daughters in Egypt?

A woman whose husband has died is not permitted to leave the marital home during her 'iddah (waiting period) except out of necessity. Her 'iddah is until she gives birth if she is pregnant, or four months and ten days if she is not pregnant, not three months. She must remain in her husband's home until the 'iddah ends, after which she may travel with a mahram.