Make it fun for your little girl... If you really want her to learn by singing the song, make the singing fun & interesting for her. Never make it a 'task' for her! A kid at this age don't need a A-Z memorising task! Kids won't learn anything unless they find it fun & interesting. Don't force upon her. If she doesn't like to sing, let her go and do other things she likes! She can't sign LMNOP,, so what? Don't show any frustration towards her... Even if she shows it on herself, cheer her up and tell her she's done so well and nevermind the rest!
My view is: like what assuiemum & lesliefu said, I won't mind her not being able to know the A-Z seqence, not really a must for 3-year-old. It's better if she can recognise the letters and understands Apple begins with a "A". Take it easy! When she goes to school, she will know it....