What are the Sharia guidelines for a husband and wife in a situation where the first wife refuses polygamy, and what is their religious duty given her refusal to communicate or cohabit?

What we advise is for you to be gentle with your first wife, advise her kindly, and be patient with her. And for the first wife to be rational and not surrender to jealousy, thus wronging her husband and herself and scattering the family. She should seek Allah's help. If the husband has treated her well, she should reciprocate with kindness and overlook what she perceives as ill-treatment, for ingratitude towards one's spouse is a sin and a blameworthy characteristic. The husband must be just between his two wives and give each her due with kindness, and the wife must obey him in what is good and not withhold his right.