"refund"; a "return" is your proof of income that calculates the refund.
If you are unmarried living together, how to pay the least tax can be complicated. Because the father pays more than half of the household expenses (rent, food, etc.) then the father could use head of household status if he claimed the child as a dependent. That has lower tax rates. You can only use the filing status "single" -- if you have been claiming head of household, you've probably been doing it wrong.
On the other hand, if you qualify for earned income credit and the father does not, that may result in your refund being larger than the refund he would get if he claimed the child and head of household.
The only way to know exactly which is better is to test is both ways. You would need 4 tax returns;
mother single no dependent + father HOH with dependent
mother single with dependent + father single no dependent
Since you will end up filing two returns, I recommend buying Turbotax Deluxe as a CD or downloadable installer and installing it on your own computer. You have to pay up front, but the desktop version can prepare and e-file up to 5 returns for the same original price. (There is an extra fee for state e-filing, but you can skip this fee by printing your state returns and mailing them in.) With the desktop version you can also make different test files since each tax return is a separate document. (Only file one per person when you decide what to do.)
Turbotax online charges a separate fee for each return and is not cost-effective if you have more than one return to file, unless you qualify to file for free.
