What about finding out what home groups the other church runs, and starting to attend one of those during the week sometime, while continuing to go to your family church on Sundays? That way you would continue to maintain all the connections that you have to the people there, and avoid upsetting your family so maintain your family relationships too, while still gaining the fellowship of a whole new group of people. You'd then be learning about God from two different denominational perspectives at the same time, which may give you opportunities to compare and contrast, and grow further in your understanding.