My parent claiming my kids

Can my mom claim my 2 kids, we live in hud housing tho she has literally paid for everything i have not made over 4,050 not even close. She has helped with utilities and rent and such. So can she put they lived with her the whole year since she kept the roof over our heads. When we put they didn't live with he she doesn't get a return backt hat makes up for the amount she did put in this year for them.