Your recipe is excellent, Keltic would do well to try it when he/she is not in such a rush. I am going to try your dumpling recipe because mine has failed the last few times I have tried it. Mine is for drop dumplings not rolled dumplings. I have gotten so discouraged with my dumplings that I have started using Grand original canned biscuits (not the buttered ones).
One poster's suggestion to cover the stockpot with a glass pie plate is a very good one. And, the poster is exactly correct: don't lift the lid while the dumplings are cooking.
Might I suggest using a bit more butter, or even Crisco, in your dumpling dough. If your dumplings are falling apart, then it **sounds** like the dough was very loose to start. Figure out a way (one idea above) to tighten up the dough, and I'll wager $20 to a cold beer your dumplings won't be falling apart. If all else fails, ask your local bakery -- they'll know for certain how to fix your dough!
Best wishes and FReegards!