Is it permissible for a young widow to move in with her mother-in-law, in a house where her married son also resides, given that she has another option, which is to live alone with her children?

It is better to remain in Kuwait with your family and mahrams, and it is not obligatory to move to live with your mother-in-law in Oman, especially given the fear of fitna (temptation/strife) if you were to temporarily reside in her house where her son also lives. Maintaining kinship ties can be done through visits, correspondence, and communication, and "So fear Allah as much as you are able." If it becomes necessary to move to Oman for legitimate reasons, then there is no harm, provided that there is security from fitna, though remaining with your family is still better and safer.