I think it is possible to bring them, as long as you meet the required salary bracket for family visa status, and you have the documents to support your plea.

I have encountered one case wherein the kids were sponsored by their mom in the absence of a husband (but she is an American so maybe it was an exceptional case for her). Ask for document support from your company liaison officer so your desire to bring your kids can be justified.

For your mom, they have a ruling here that anyone above 60 is not eligible even for a visit visa. Perhaps it is for health reasons, that's why even those who have stayed here all their life have to go when they reach 60.