You sing it to your kids once in a while, correct?

Try this idea from my wife (who says she got it from somewhere else):

When you get to the ee – i – ee – i – oh part, change it to A – E – I – O – U.

Then with almost no effort on your part (or their’s) you will have taught them the vowels, in order.

This will be valuable when it’s time for them to learn to read.