Is it permissible for a man in a misyar marriage to take his wife to his home and spend on her during her stay, then return her to her family's home, and does this act change the designation of the marriage?

Misr marriage is valid if it fulfills the conditions of a valid marriage, and its effects, such as the wife's entitlement to housing and maintenance, apply, unless she willingly waives her right. She may move to live with her husband unless she stipulated that she remain in her family's home.