Amedment for tax return form

what's the problem with getting a SSN for them?

see this link

https://www.ssa.gov/pubs/EN-05-10023.pdf.  it has a phone number to call if you have questions

if you haven't filed already, you have until 10/15/19

you could always file without claiming them  and amend later.

mailing a return listing them without their SSN's  is only going to result in notices from the IRS and possibly problems later when you go to amend.   

by the way,  if the other parent has their SSN but won't tell you what they are and  you are on the birth certificates, the SSA should release the numbers to you but you may have to set up an office visit to prove that you are who you say you are.   if you are not on them, consult a lawyer.   

if you are the noncustodial parent, without a form 8332 from the custodial parent, yo won't be able to claim them 

Sometimes, if you claimed dependent care expenses or education expenses on the children, clearing them from your "MY Info" section isn't enough. You have to work through the return and delete anything and everything related to dependent credits and deductions. It would be necessary to work through the return again anyway, because that's the only way the program can "re-do" the math for any credits or deductions the dependents may have qualified you for.

Besides, the only way you could have even completed a section such as the education section, would be if you had entered a bogus SSN just so you could "work it through". So that's another reason you'll have to work it all through again.

It can be tricky to do this right. So you might find it easier and simpler to just clear the return entirely and start over from scratch.