Can I claim my sister as a dependent if the custodial parent is receiving child support?

Hi, hope someone can help me with my confusion. This is my third year filing my tax return. Some changes happened which I can't seem to find the answer to my question else where. 

Basically I am the only one with income in my residence, living with my mother and sister. Mother got divorced and is receiving child support. The court order says she can claim my sister as a dependent on odd years, and the non-custodial parent can claim her on even years. 

My question is since I am the one with the most income as my mother only receives child support, do I claim my sister as a dependent or does my mother have to file her own tax return.

My mother has been unemployed for a couple years. I'm 20 incase that info helps.