The relaxed hand should always be your goal. If your stiff your going to sink a bit. Also that stiff hand could contribute to the head and spine not being in line (i.e. laser-like fashion).
With regards to the swim cap, if you put it on dry then ari might have got underneath causing it too feel a bit odd. I use a silicon cap and wet my hair and cap before I put it on, never had a problem. You might try a latex one instead.