Leaving your kids at home doesn't mean you wouldn't want to be with them, that you don't love them and that you are over there having a glamorous life
First of all, most people go abroad because of work, not really because they want to live there. If you are a mother who left, you are working full time and, most of the time, in a bad place to send money home so that your kid can have a nice life. You being there doesn't mean that you want your kid living in a bad neighborhood in a tiny apartment with you. And also, if you had your kid there you wouldn't be able to watch her/him; You'd have to hire someone anyway, a stranger! Mothers have some sort of peace of mind when they leave their kids home with a trusted relative, usually the grandma. By the way, if you wanna know what your kid's up to, you can call a neighbor and they will surely tell you.
Then there's the parents who are afraid of "losing" their kids to drugs and other influences. While in the DR you can have control over your kids, even if they're close to or older than 18. I've heard many concerned parents say that their afraid of bringing their kids to NY! There is also fear of schools there, with the bullying going on. Here you know that your kids are in school and you can be sure that no one is going to stab them, shoot them or beat them up and send them to the hospital.
Of course, many parents still "lose" their kids while in the DR. Sending stuff isn't isn't enough and the love of a trusted relative can't make up for a mother but for most people this works.