Yes, you will get your money "on time". If you file first you will get the money in the normal e-filing time. If she gets in first, you will get your money in the normal paper filing time. See details below*.
You should be aware that, starting this year, there is a delay, in getting refunds, for all people claiming child based refundable credits. See https://www.irs.gov/uac/as-holidays-approach-irs-reminds-taxpayers-of-refund-delays-in-2017
You should also be aware you do not have an automatic and exclusive right to claim your own child. Under certain circumstances, your mother can actually be entitled to claim your daughter. If you want more details, provide more info. where do you live, how old are you, what is your income, are you a student.
You cannot prevent someone else from claiming your child, other than discussing it with them in advance. If the three of you live together, you usually (depending on the details) are allowed a choice. The smart thing to do is do trial returns both ways and see which way the family comes out best.
*If someone else claimed your
child inappropriately, and if they file first, your return will be rejected if
e-filed. You would then need to file a return on paper, claiming the
child as appropriate. The IRS will process your return and send you
your refund, in the normal time. Shortly (up to a year)
thereafter, you'll receive a letter from the IRS, stating that your
child was claimed on another return. It will tell you that if you made a
mistake to file an amended return and if you didn't make a mistake to do
nothing. The other party will get the same letter you did. If one of you
doesn't file an amended return, unclaiming the child, the next letter, from the
IRS, will require you to provide proof. Be sure to reply in a timely manner.
Winner gets the tax benefits; loser gets to pay
the IRS back with penalties and interest.
www.eitc.irs.gov/EITCCentral/f886-h-dep.pdf
