Hi, saw your post and just wanted to say I'm sorry you're feeling so low right now. Having lived abroad myself, and experiencing this kind of homesickness, I understand how wrenching it is.
Never been to Singapore. What's it like there? What do you and your husband and children do when you're not at work? Have you met any other expats?
I read that 'sacrifice' means giving up something you love now for something you'll be glad you did later. Or something like that. I think your goals are admirable and the fact that you are sacrificing time with your Mum and friends, and home, reflects your commitment and dedication as a parent to provide the best possible future that you can for your family.
Do you keep a journal? If not, I encourage you to try it. Write as if writing to a friend...or your Mum, even. It can help make you feel closer if you can feel that you can 'talk' at any time.
Do you use Skype or Snapchat or similar? I appreciate the time difference but maybe Mum or a friend won't mind staying up late or getting up specially early just once a week or so, so that you can connect with home?
I know its really difficult and when I lived abroad I had no one around me to do anything with, and sadly that didn't change the whole time I was there, so I do know how isolating it feels.
Consider a 'checking in' thread here, too! I'm sure there are lots of people who are up at all hours and wouldn't mind 'chatting' if you pop in. Like me 
Sending you hugs 