Awesome!! Something i can help out with. Well, do you know how to dance? Because to me playing rhythm while singing is the same as dancing while singing, you line up your chords with the vocals just like you would dance steps.
Ok, thats a cheesy analogy. But, try singing along to a song you know how to play and play air guitar while you do it, or just play real guitar and focus on the vocals. Once you learn how to sing and play, even complex things get easy. Think of your strumming as 'keeping time' just like if you tapped your foot. What type of music do you listen to? i'll recommend a song to start with if you like. After a while, even metallica riffs and dave matthews stuff is just like walkin and chewin gum.

Atomic