SARAH VINE: Kate's on the mend, so what a pity this image is fuelling yet more rumours

Finally. After weeks of growing speculation about the health of the Princess of Wales, a sign that she is, if not quite ready to go back to her royal duties, at the very least truly on the mend.

Here she is all smiles for a characteristically stylish Mother's Day snap with her three children. She has even managed to slip into a pair of skinny jeans for the occasion. That's quite a feat when you are recovering from a major operation. And very her.

I note also that she is not wearing her wedding and engagement rings. No doubt she was required to take them off for the operation, and kept them off for medical reasons.

Or maybe she's lost a bit of weight, as many do after surgery, and doesn't want to risk them slipping off her finger. Either way, let's hope they are somewhere safe.

But it's great to see her looking so well, not least because this kind of picture is exactly what we've all been waiting for: something to scotch all those absurd conspiracy theories doing the rounds online.

Kate is positively blooming, all smiles for a characteristically stylish Mother's Day snap with her three children

Or is it? When it was released by the Palace early yesterday morning, I – like many – was delighted. Here, finally, was the antidote to all that nonsense.

But by yesterday evening, this cheery Mother's Day snap had taken on a whole new dimension. Instead of dampening the rumours, it appears to have only added to them — thanks to some distinctly cack-handed attempts at retouching.

Whoever is in charge of Photoshop at Kensington Palace might like to think about taking a brush-up course. Because it is not the first time they've made a hash of things (see the Waleses' Christmas card and Prince Louis's missing finger). This time, however, they have excelled themselves.

Princess Charlotte's wrist, boot, sleeve; Louis's fingers (poor kid, not again) – and even the Princess's hair. It's all just a bit… well, wonky.

So much so that top foreign picture agencies have ordered for it to be withdrawn from circulation, on the grounds that it has been digitally altered.

And so what ought to have been the perfect response to that highly intrusive paparazzo shot taken of her supposedly on the school run last week (which the British Press, quite rightly, wouldn't touch with a barge pole) has ended up fuelling even more speculation.

Added to the fact the Palace has not managed her convalescence very well (in particular that mix-up with the Ministry of Defence, which said the princess would be appearing in June at Trooping the Colour, only to find itself slapped down by Kensington Palace), it all points to yet another failure on the part of whoever is advising the Waleses.

And let's not forget that weird incident when Prince William cancelled his attendance at his godfather King Constantine of Greece's memorial service at the last minute. Annoying as it must be for William, he can't do things like that and not expect a reaction.

I'm not sure the Waleses realise quite how central to the Royal Family they are now, at a time when the King is undergoing treatment for cancer. His Majesty is, by all accounts, doing well — indeed, I am told he is in high spirits. Still, the baton passes, however temporarily, to his son.

And despite the best efforts of the Montecito moaners, Harry and Meghan, to cast the Princess of Wales in a negative light, most British people view her with great affection.

The nation is invested in the Princess, and in William, and we care about her. It's good to see her smiling face, and we wish her all the best with her recovery. But whoever is behind these unforced errors must get their house in order, pronto.