It's not for wa noises, the problem (for me XD) is the way you pronounce "R". You seem to say "haw" instead of "R"! XD
Try to read this " Marrrrio", with many "R"s...;p I think this must be difficult for you!=D
It depends on where in America you're from. Us Italian Americans who live here in New York always slur our Rs together, thus producing the sound you're talking about. Me, I can avoid that easily, it's just that most of the time I don't because it's in my blood. I'm actually capable of putting on many different faux accents, although I am actually unable to roll my Rs the way you just described in that last sentence.