How can one deal with a mother who does not behave well, gives her money to strangers, and suddenly cries and gets emotional, causing embarrassment to the family, especially with the wife and sisters-in-law feeling alienated from this mother, and is it preferable to divorce the wife in this case?

The mother's right is great, and honoring her is one of the most obligatory duties. The wife also has a right that must not be neglected. Therefore, it is necessary to combine honoring the mother with good treatment of the wife, giving each their due. The relationship between them should be mended, and it should be explained to the wife that it is part of her good character to be kind to her husband's family and to help him honor his parents. Divorce is not recommended, and there is no real contradiction between keeping the wife and honoring the mother.