I don't think there's anything wrong with how your brain is wired. You are used to singing without a guitar, so bringing the guitar into the mix is throwing you off.

There have been times where I would learn a solo and be able to play it flawlessly by myself and over a backing track. I would go to rehearsal with my band and fail miserably! The ONLY difference was I was now playing in a different environment with the band backing me. With some practice with the band, it all came together.

I would take it a tiny step at a time. It may sound ridiculous, but try this:
- Sitting or standing how you would with the guitar (but without holding the guitar), sing the song.
- Sing the song holding the guitar, but don't play.
- Sing the song and just fret the chords...don't strum them.
- Sing the song and single strum each chord when the chords change.
- Sing the song and play the guitar as you plan to

This will break it down for you and you can work on each aspect of it separately.