Martyn, I'm sure you did not intend the "Erm..." at the start of your post to come across as sarcasm, although I must confess to me it did sound that way; in the interest of happy discourse, allow me to expand my post a bit.
I'm sure that Louis and Edwina's marriage was complex--most marriages are, especially one that is long in duration, and with the added layer of historical events and personages that played so significantly in their marriage. And in any marriage, there are often disagreements, there may be infidelities by one or both partners (and there may very well have been from time to time in the Mountbatten marriage, by both of them), and things may not always be rosy.
But the Mountbattens had a strong and committed partnership. Mountbatten himself has described Edwina as his true love, in words to that effect. They relied on each other, they respected each other, and if doing that for thirty or forty years, or however long it was they were married before she died, doesn't constitute a long and happy marriage, then God help the state of matrimony.