This may not apply to guitar playing, so feel free to ignore. My experience is playing piano and singing.

I usually play very simply "under" my singing.

When I first tried to play and sing at the same time, I HAD to play very simply for the whole song because it was hard to think about everything at once. After a lot of practice, I got much smoother at it, but I still play more simply while I'm singing, so as not to have the piano compete with my voice. I put in more complicated stuff as fills between phrases, while I'm inhaling, I guess. When I listen to a recording now, I think, wow, how do I play THAT and sing THAT at the same time, because I now often improvise a melody on the piano that harmonizes with what I'm singing, without really thinking about it, just because I feel like it at the moment, and often my piano rhythms are very different from what I'm singing. It comes easy now, compared to when I started. I'm playing two instruments at once and my brain can handle it.

The only real drawback for me now is that I sing much better if I can stand up, and I like to sit at the piano. That's not about coordination, though.

It helped me a lot to simplify what I played when I was first starting to perform with piano and voice at the same time.

Maybe you've already come a long way--I notice you posted your question in April! If you've been practicing, I'm sure you've noticed how quickly it starts to get easier and better! --Jean