Help me to love my peonies

When we moved in three years ago there were a three large peonies: two in a slightly shaded bed, one in full sun.  I love the colour of the emerging shoots but we don't get many flowers and they flop over in a mass of foliage.

Would splitting them increase the flowering?  If I moved them onto poorer, shallow soil would that help redress the leaf/flower balance and stop them flopping so badly?  It's pretty windy here - is that the problem?  We are in Fife, five miles from the sea.

Many thanks.

Give them support now before they get too tall. The framework will soon disappear as the plant grows. If it rains when the flowers begin to open or are open gently incline the flowers and tip the water out, so they don't rot and the flowers last longer. Feed them after they flower to build up the store for next year's flowers.

I have supports put in, but the peonies always overwhelm them and fall over anyway.  I suppose I'm impatient with plants that can't stand up on their own.....