Have you tried L'Horizon? This is on PS canyon drive, they have the JACK WRATHER HOUSE, with a private pool, two bedrooms, bar, there is a jacuzzi & large pool also. It's VERY quiet and secluded. Try www.palmsprings.com they have good rates.
The Givenchy is now Le Parker Meridian and it is lush. You will have to pay a lot more now that it's Le Parker(they raised the rates considerably)and it's not secluded or very private, unless you get the Villas, but no private pool.
I would try the River at Rancho Mirage which has many higher end restaurants to choose from.

In any case good luck and you'll love the weather there in April.