Hi
Actually the hotel IS in the transit zone, but on the third floor, whereas the shops and entertainment areas are on the second.Is that what you mean Atilla?
The bathrooms are stocked with basic toiletries and towels as in all hotels. You might just want to pack toothbrushes/change of clothes/swimsuit. You can't take liquids through customs clearance in UK and singapore that's why I suggested going to pharmacy in transit zone. They are well stocked in travel size basics such as toothpaste and sun lotion.
Travelling between T1 & T2 takes about 20 seconds via skytrain so really no sweat. Finding your way/walking around the shopping/transit zone is also very easy, but take your time, it's big.
When you land, go to transit desk. They'll issue your boarding passes for the next day and redirect your luggage. very helpful staff.
I second the idea of spending the day in singapore.
The zoo is great and they have shuttles running back and forth from/to airport.
It's on the other side of the island so journey is about 40mn.
If you do not want to venture too far, then yes, east coast park is the place. About 10mn from airport.
Beach (overlooking supertankers), bicycle/rollerbalding rentals, lots of food stalls/snacks/restaurants.
Taxis are cheap and plentiful as said before.
I live in singapore so if you need more info, let me know.
How old are your kids?