"head of house hold for half the year" Did your Mom work the other half?
"she won’t or can’t be reporting taxes or my sibilinos (3 of them) since she is not a resident;" She is required to claim her income, even if she is undocumented..
One of the keys here is that, in order to claim HOH, you must have provided more than 50% of the support for the entire household for the entire year. Let's assume for a moment that you didn't work.. How would the bills have been paid? Alimony? Child Support? Disability benefits? Govt assistance? Other? Now add in your income. Is it more than the total of all those?
