If you're looking for stunning tropical beaches and lovely blue seas, Port Dickson is not it. Tolerable at best, at worst if the currents are unfavourable the beaches there can get oily/littered. Port Dickson's only main selling point is proximity to KL. But if you do want to go there, the place to stay is the Lexis Hibiscus.
The West coast of Peninsular Malaysia is not as "seasonal" as the East coast, so even in the "rainy" season (which December is not, on the West coast) you will rarely experience enough rain to stop your activities all day. Not to mention that rain in the tropics is (1) warm and (2) intense but brief, an hour or so at a time usually in the late afternoon.
So if you want beachy island life in December, I concur with everybody else - go to Langkawi, it's gorgeous and the beaches are almost as good as the East coast islands (the water is less magically clear and turquoise). If you want a bit of beachy island life plus a lot of culture/food/colonial history, go to Penang*.
People generally don't go to the East coast beaches, or the East coast islands, during the monsoon season unless they like surfing in grey seas. And IIRC a lot of the stuff will be closed or reduced provision during the monsoon anyway.
*As you have young children, check out Escape Penang water park which is nestled into a forest setting, there's a ski lift through the canopy to the top of a hill, there's Go Ape type stuff, there's the world's longest water slide, there's awesome splash pools. It's marvellous and my DC (now teens) are obsessed with it.
PS. Let me know if you want Penang accommodation recommendations.