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

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?

If this is your husband's house, you can't say no. It's best if you stay away from the private matters of your husband's cousin's daughter so that she stays away from yours. Let there be a separate space for her where she can do her own work and both of you stay away from each others private matters. From the start set the boundaries so that problems do not arise.