We stayed at the hotel Condessa de Bahia in Playa del Moro and the hotel next door had a wooded area on the beach.It was called Platja d Or and was then a Thomson Gold hotel.I think its now AI.There was an annex on the beach and between it and the main hotel was a garden area with pine trees.

I was going to say the Condesa de la Bahia though it's not self -catering.....

I think the Platja D'or is still adults only so no good with the baby.

However the C de la B is not quite as far south as Playa de Muro, so you are still within walking distance of the port of Alcudia and the bars/restaurants etc. there.

But here is definitely a lot of shady beach near C de la B

re other resorts there is a shady beach along the Pine Walk in Puerto Pollensa, you might find the Playa Mar or Puerto Azul (both Thomson Superfamily) fit the bill. Puerto Azul also has a big shady canopy in the pool area. But the beach is narrow...although I don't suppose the baby will be making sandcastles yet For the adults there are bars etc. in PP but not nightclubs.

Going a bit further towards Alcudia from Playa de Muro is the Orquidea Playa, which is right on the beach and does SC. There are trees to be found along the stretch of beach while the pool area is also partly shaded. At this hotel, you would be just a few minutes from the nightlife of the Bellevue area

As regards Puerto Pollensa. The Pinewalk beach, while attractive, is very narrow. There are clubs though in PP e.g. Kudos, Tukys, Chivas Disco.