It is amazing how "thin" batting (or wadding, as you Brits call it :lol: ) doesn't seem so thin when we get it layered and start quilting. I used to think I needed fat batting too, but the best quilts have thinner batts and then "puff up" some when we wash them. As heart breaking as it may seem, I think you are going to be much happier if you take your quilt apart and try it again with the thinner batt.
Sewaholic's advice is great---pin well-all over-and then be sure to use a walking foot when you are machine quilting. This should eliminate any problems you were having.