Her father's sister's son would carry his father's Y DNA not the father line you are looking for. The Y DNA would have to come from your suspected sister's father's brother. Also Y DNA won't prove paternity and will only prove male line so its possible this person you match could be your 1st cousin or a 1/2 sibling. There maybe other ways to be able to figure out if you were 1/2 siblings or 1st cousins but I would ask an expert on this issue. Its much easier to prove two sisters share same father through x chrome matching.

PS I also agree with advice DPotts has given you