You are confusing phrasing with groove.
The drums are forming a groove and the chords are locked to that groove. You then want to sing a phrase over that groove.
Have you ever noticed that a lot of people get a singer or a guitar player but not both at same time.
You need to be able to play those chord changes in your sleep THEN sing over them. I would suggest to go really slow. She is singing over the chords too but her phrasing is not locked to the groove like yours.
You are probably coming closer to singing a bass line when in fact you want to sing a floating melody.
Try playing three chords or however many suits what you are doing. then have a set of words that are normally sung there the way you would like to hear them////
So you have say
G ----------- C ---------- D ------------
This is my melodyyyyyyyyyyyyyyyy
Now, just play the chords over and over.
Once you get the groove going just sing the word "This" but hold it for all three chords.
G--------------C--------------D---------------
Thisssssssssssssssssssssssssssssssss
In your head try to "hear" the words "This is my melodyyyyyyyyy"
Basically you will be singing a tied whole note for three bars.
Do that a bit. then ad the next word...
"This is..............." but this time around try it different way WITHOUT screwing up your strumming.
G------------------C----------------D-----------------
Thissssss issssssssssssssssssssssssssssss
G------------------C------------------D---------------
ThisssssssssssssssssIssssssss......................
etc. IOW be able to This is in all sorts of different ways in time but not necessarily locked to when chords change.
Add words, repeat. After a while the chord strumming will disappear. Almost like someone else is playing. At that point you should be able to sing all sorts of "versions" of the lyrics and not get out of time or mess up a chord.
G---------------------C------------------D-------------------
this is my melody This is my melodyyyyyyyyyyyyyy
Make sense? Your brain is too locked up to the playing and not the singling. After you separate the two you will actually be able to influence your strumming by how you are singing for little nuances and embellishments. If you get really good you might even be able to free your mind and dance around in circles like the t girl.
Or... if you get really really good... you might be able to do this.
http://www.youtube.com/watch?v=PLunBk4bOzUThis falls under the category of "Free your mind and your ass will follow" .... oh,,, and before that you have to practice your ass off.