Answer: Pinching mums back should encourge lots of new shoots which should be shorter and sturdier than if you didn't pinch at all. It will also result in a riot of flower buds, as you have discovered. But, these opened flowers can become heavy with rainwater (or water from the hose) and bend over with the weight. To overcome this top-heavy tendency, try pinching as usual, then as the flower buds begin to form, pinch out all but the top-most flower bud. This will give you fewer, but larger flowers, each on a single stem. The stem should be strong enough to hold the flower upright, even when it is fully grown and soaked with rain.
Or, if you'd rather not pinch the flower buds out, you can support the plants with peony cages. These metal units are designed to fit over young plants; train individual stems up through the openings and when the plants are in bloom, you'll barely see the supporting grid.
Enjoy your mums!
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