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?

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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.