My husband wants to bring home his cousin sister’s, 19 year old daughter to stay at our house for 5-6 years for her studies, I am not comfortable with this as I think it may distrupt our couple life among other things, am I obligated in Islam to do so?

You need to discuss the social aspects and how it would impact your family structure and also the concept of maintaining modesty of your husband's cousin at all times during her stay. You are not obligated to keep her according to our Shariah. It is important that you discuss this matter with rationale and have mutual understanding so not to cause any conflict in your marital relationship