I would think its more likely they offer a laundry service than for there to be actual facilities to do it yourself, I've certainly never come across any Caribbean hotel that has a laundrette so far anyway.
There is usually a bag in the wardrobe with a price list per item, I'm sorry I can't remember the prices from the last time I was in the DR.
I usually take a bottle of washing liquid from Superdrug and rinse shorts, tops and undies, then roll them in a towel, they don't usually take very long to dry although you might want to take a couple of hangers as the hotel ones usually have no hooks. I generally hang them on the shower rail and let them drip in the bath but you could put them on the balcony if you have one.
I'm a big lady and I've managed with 15kg before, most days are spent in swimwear and sarong or shorts and vest tops which don't take up that much room. Its too hot for heavy clothes so strappy lightweight dresses for the evening are great with a few pairs of crop trousers with more vest tops and you're sorted.
My usual problem with weight is the shampoo and conditioner and creams and potions, they weigh a ton so simply buy them in Boots after you have gone through security and put them in hand luggage but don't forget to make a list, they cost a fortune to buy out there, leave whats left for the maids. I've found a lot of people actually leave clothing for the maids to make room for souvenirs and they are very grateful.
If you are a tea drinker you might want to consider taking some tea bags, theirs tasted like pond water to me, their coffee is usually great though.
If you're taking children you might like to be aware that sweets and snacks are very expensive, I put my medication in a Tupperware type container with a lid, tip it in a drawer when I get there and then use that to store little biscuits or cakes from the restaurant, you're not robbing them being as its AI. If you store food in any other way in your room you stand the chance of getting invaded by ants.
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( this is the reason some restaurants don't like to you to take food out so you have to be a bit discreet if you do)
A lot of the cocktails contain coconut milk which is a natural laxative so beware.
I'm honestly not insulting you by saying be very vigilant in washing your hands before eating and after every visit to the loo. There are sometimes outbreaks of diarrhoea and sickness in DR hotels and its spread because the tropical heat makes germs grow so quickly. All it take is someone with a funny tummy leaving "something" behind on the loo handle when they flush and the next person that touches it gets it on their hands. If the soap runs out in the rest rooms complain and find somewhere else to wash your hands. Its expensive to be sick in the DR and you don't want your holiday spoilt. I'm sorry if you think I'm stating the obvious but people tend to blame the food and from my own observations I'd bet its more a lack of hygiene in many cases.
Please remember, the DR is a third world country, its nothing like the European resorts (thank goodness
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) there is poverty and it upsets some people to see it but tourism is providing an income for these wonderful, friendly people and once you are in the resort you won't notice it.