Half your luck bubbaluci and if it holds you might just miss worst of southern Malaysia Monsoon season, http://www.myoutdoor.com/desaru/promotion.htm indicating November to March., probably best to get there via the ferry from Singapore, Changi ferry terminal as train does not go too close and so you'd have to get a train/bus or buses.

Singapore is essentially much the same year round being on the equator and so it'll be very muggy - something that will not go down too well with your own bubba.
You ought to try him/her out on cuddling to a bottle of chilled water, heard it helps them get through the irrates of warmer weather, and not a hotel, but good as if not better than some and I wish I had known of the Sibgapore YWCA before I stayed in a real black hole of Calcutta on my first backpacking to there - http://nof.ywca.org.sg/ , looks good and they even show childcare, and you cannot ask for a better location down near the river/parks and you'll certainly notice a difference along the river and elsewhere.
Their pricing is not showing nor their booking opening to check there but a two day one night retreay package shows as only $115, so I'd reckon on room rates being pretty good, $S ~= $A at moment and more than $MR2 so Desaru will be well under $100.

http://app.www.sg/ has some good info as well as a mao under Singapore at a Glance.

Other things to do in Singapore other than shopping and shopping is Sentosa Island, and there's a little island on eastern end of main island too that could be worth a trip to somewhere not so developed, Chinese/Japenese Gardens, the Zoo and having breakfast with the Orangatans if they still do that and you can manage it with the littlies.

You might just want to get out very early to have a look about with the kids before it gets too warm for them, and then head for comfort of air conditioning, and then out again in the late afternoon/evening.