Thank you for giving me the opportunity to assist you. I will give the best answer that I can with the information provided.
I have read your prior question---Can you tell me how old your daughter is, if she lived with you for the entire year in 2010---
Also, Your son in law absolutely cannot use the children as qualifying children for earned income credit. He cannot get earned income credit at all if he uses married filing separately status--which is his only choice presuming he has no other children---unless your daughter chooses to file jointly with him.
I need some additional information so I can figure out the correct answers for you.
Can you tell me how old your daughter is, how much income she earns, how long she was a full time student last year---and how long she lived with you?
In regards XXXXX XXXXX head of household question--I don't know what you mean by if she files "with him as head of household"---that wouldn't be an option if they filed a joint return.
If your daughter was enrolled as a full time student for any part of 5 calendar months during 2010---which would count if she was enrolled in August, but not if enrolled in September---then she would be your qualifying child and not allowed to take her own exemption unless she filed jointly with her husband.
If she was only a full time student for 4 months of the year, if she earned more than $3650 in gross income (aid/student loan, etc. grants for tuition does not count toward gross income) then she would not be able to be claimed by you as a dependent.
Someone telling you that she cannot take earned income credit since she doesn't have a W2 is not entirely correct----she could claim the credit, but if her credit was investigated she would need proof of earning---such as canceled checks, log of jobs done and for whom, dates---etc.
If she does not file a joint return with her spouse, she is not eligible for earned income credit regardless----since her only option would be to file married separate, and the credit is not allowed for married separate filing status.
She cannot file head of household, because she did not pay more than 1/2 the cost of keeping up the household.
If you are looking to receive the best tax benefit for your situation you should consider--
A. Claiming your grandchildren (and daughter if she meets dependency requirements) and using the refund to pay your past tax debt---you are still receiving the benefits by reducing your debt and reducing penalties and interest that pile up.
B. Have your daughter file a joint return with husband. If there is fear of him taking the entire refund, you are allowed to file a form (electronically) that will split the refund into two different bank accounts---half could go into hers, and half could go into his.
No, I'm sorry if I confused you.
What I meant was that you could consider either A or B.
However----You could claim the children as dependents and let the parents file a joint return together. You can not mix the children and put them on your return AND your daughters' return. Since the children lived with you and with their mother--you cannot pick and choose benefits, it's either all or nothing. You cannot claim them as dependents and have the mother and father file a joint return and claim them for EIC.
Your additional information confirms that your daughter is your qualifying child and may be taken as a dependent by you.