you can't efile any returns. first, efiling is closed for 2019 and prior years. second, the fact your kids have been claimed would prevent you from efiling in any case. online preparation is closed for 2019 and prior so you need to purchase either the CD (only if you have a cd drive on your computer) or purchase for download. note that it's too late to file 2016. the last date for filing was 10/15/2020.
you'll need to file form 14039.
Whenever a Social Security number has already been used on a tax return, no one else can e-file using that SSN, so your e-file would be rejected if someone claimed your child. The remedy is to print sign and mail your own return that claims your child(ren). Then the IRS sorts it out and sends letters to each of you and you get to prove that you are the person who can rightfully claim the children. The other person will be subject to penalties and repayment of refunds they have received fraudulently.
You say you have to file for three years back. Each year must be filed separately. Do not try to combine those tax returns in any way, not even by putting them in the same envelopes when you mail them.
To file a return for a prior tax year
If you need to prepare a return for 2017, 2018 or 2019 you can purchase and download desktop software to do it, then print, sign, and mail the return(s)
You may also want to explore purchasing the software from various retailers such as Amazon, Costco, Best Buy, Walmart, Sam’s, etc.
Remember to prepare your state return as well—if you live in a state that has a state income tax.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.
Federal and state returns must be in separate envelopes and they are mailed to different addresses. Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.
Note: The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac. It cannot be used on a mobile device.
If you are getting a refund, there is not a penalty for filing past the deadline. If you owe taxes, the interest/penalties will be calculated by the IRS based on how much you owe and when they receive your return and payment. The IRS will bill you for this; it will not be calculated by TurboTax.