If your mom is claiming you as a dependent then you cannot claim a dependent of your own.
A child can be the “qualifying child” dependent of any close relative in the household. So, if you live with your parent, it may be better if she claims your child. Essentially you are allowed a choice. It may be worthwhile to prepare returns both ways to see which way the family comes out best.
That said, There is a rule that says IF somebody else CAN claim you as a dependent, you are not allowed to claim your own exemption. If you have sufficient income (usually more than $6350), you can & should still file taxes; you just doesn’t get your own $4050 exemption (deduction). You also don't get to claim your child as a dependent. In TurboTax, you indicate that somebody else can claim you as a dependent, at the personal information section.
So that brings up the quest of CAN you mom claim you. Based on the additional info you supplied; YES she can. So, no, it is not legally possible for her to leave you off her taxes! Technically, she can leave you off; but still cannot claim yourself or your child. The rule is if you CAN be claimed, not if you ARE claimed
