Deductions & credits

Update: My parents are divorced AND not married to anyone else. We live in Florida who does not recognise common-law marriage. They share expenses of the home ( we all live under the same roof) but my dad earns more, by like 30k. That is why he will claim my sister and I. I was just wondering if my mom qualified for the: Not a dependent ( EIC / Child Care Credit only ). I did not understand the intent to action part.