If you are not singing the correct note, you are either completely missing the intended key or most likely you are singing in 3rds, 4ths or 5ths of the intended note.
If you are singing the correct note, Your Dad could be picking up on modal changes (or even note borrowing/substituting)
They are quite popular in music. It happens when a song includes a note from a neighboring scale or key. Anytime there is a “key change” there is a “modal change” The ways to know when you are doing it are either, learn and understand the notes as you sing them. Or listen to the scales of different notes and song examples and eventually you will hear the interval changes that are unique and but very identifiable.
Say if you are singing In the key of...
C Major - C D E F G A B C
(Starting with C, ending with C)
This is also known as: “C Ionian” - Upbeat, happy & half pop songs.
If you change to the key of...
A minor - A B C D E F G A
(Starting with A, ending with A)
This is also known as: “A Aeolian” - melancholy, sad & the other half of pop songs.
Different modes, same notes, different order. It’s created a completely different emotion. There are 7 modes per set of 7 notes for each 12 keys. You don’t need to stay within the set of 7 notes to change modes,.. for example..
Changing from C Ionian(C Major) to:
C Lydian (same notes as G Major)