الجواب وبالله التوفيق      

As per the situation described in your question, Nikah between your cousin and your sister cannot take place as your mother and your cousin are considered brother and sister through the milk kinship (Raza‘i). You and your sister are considered your cousin's nieces through that relationship. Since performing Nikah with a niece related through blood (i.e. bhanji) is impermissible similarly it is haram to perform Nikah with a niece related through milk kinship. It has been mentioned in a hadith of Rasulullah Sallallaho Alyhi Wasallam:

بحرم من الرضاع ما یحرم من النسب (مشکوۃ شریف بحوالہ فتاویٰ محمودی 

واللہ اعلم  بالصواب