You are not being seen by the neighbor. You are singing with your family. You are in your own home. Ask your rov, if he thinks that you needed more than ONE of these reasons to give you a heter, much less ALL three. Providing a proper and enjoyable Shabbos atmosphere at the table for your children is more important than being overly worried about what someone in ANOTHER apartment UPSTAIRS may or may not be able to hear. At most, it is muffled noise. Unless you are Ethel Merman, your voice is HIGHLY unlikely to be distinctively heard among the others by the males upstairs. They can always outsing you with their own zmiros, if it bothers them.
Aries made good pointsm btw.