Dependenther mother gets to claim her this year as a dependent. If she files her own taxes, will her mom still be able to claim her and get whatever child tax credit there is for her

No.   A dependent is not permitted to claim a dependent of their own.   At age 17, your daughter can still be claimed as a qualified child dependent.   

 If your 17 year old has a child is being supported by you, then you can claim her and her child as dependents on your own tax return.   The person who is claiming the baby is the one who gets the child tax credit.    You will not get CTC for claiming the 17 year old --- she is too old--- but you get the $500 credit for other dependents for her.  Depending on your circumstances, you may also be able to file as Head of Household and get earned income credit or childcare credit if you paid someone to take care of the baby while you worked.

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent

https://ttlc.intuit.com/questions/3113432-who-can-i-claim-as-my-dependent  

WHO CAN I CLAIM AS A DEPENDENT?

You can claim a child, relative, friend, or fiancé (etc.) as a dependent on your 2023 taxes as long as they meet the following requirements:

Qualifying child

• They're related to you.
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They're under the age of 19 (or 24 for full-time students).
• No age limit for permanently and totally disabled children.
• They lived with you for more than half the year (exceptions apply).
• They didn't provide more than half of their own support for the year.

Qualifying relative

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year (exceptions apply).
• They made less than $4,700 in 2023.
• You provided more than half of their financial support.

When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them. There may be other tax benefits you can get when you claim a dependent.

To claim a grandchild as your dependent

When you enter the child’s name in My Info, you will be asked “What’s your relationship to  [child’s name]?”  

           Choose “another person”

            a drop down menu will appear that lets you choose grandchild

And....to be clear----all of the child-related credits are based on having income from working.   Without income on a W-2 or self-employment income, you do not get child-related credits.

And....since your daughter CAN be claimed as a dependent, if she filed and said she cannot be claimed --- she needs to amend her tax return.   And re-pay any credit given to her by the IRS or state.   If she filed first it has blocked the parent who can claim her from being able to e-file this year, so that parent will need to file by mail.  Waiting for the amended return to be processed will do no good; the correct return can be filed by mail at any time.

Yes, if your daughter indicates on her return that someone can claim her as a dependent, then her parent will not be blocked from claiming her. TurboTax asks the user whether someone can claim them as a dependent.

If she filed a return and didn't indicate that she is a dependent, then when someone tries to claim her, their return will be rejected from e-filing.

See this IRS webpage as well as the info shared by @xmasbaby0 above for more information on who qualifies for the Child Tax Credit.

@danielabdella 

Q. My 17 year old daughter  will file her own tax return this year, will her mom still be able to claim her and get whatever child tax credit there is for her?

A. Yes. A dependent can file their own separate tax return. They just check a box on that form saying they can be a dependent on someone else's return*.

Q. Does mom still get the child tax credit?

A.  Yes, but not exactly. A dependent filing their own tax return does not eliminate the parent getting the dependent credit. But, because she turned 17, the parent no longer gets the generous (up to $2000) child tax credit. Instead, the parent gets the (up to) $500 "Credit for Other Dependents". 

*Furthermore, there is a rule that says IF somebody else CAN claim him as a dependent, he is not allowed to claim himself. If he has sufficient income (usually more than $13,850), he can & should still file taxes. In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.  TT will check that box on form 1040.

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

With the tax law change, effective 2018, most dependents will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased.