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@emilymcbroom-136 - this is the type of documentation the IRS is going to ask both of you in order to determine who is able to claim the children. 

 

https://www.irs.gov/pub/irs-pdf/f14815.pdf

 

read the instructions in the left column closely; not all will apply to you.  assuming these children are under 17 years old and born in the US,  then only #3 and #4 will pertain to you. #3 should be easy and #4 is the critical one as whomever can prove the child lived with for more than 6 months is most likely to win the case.  You did state one child lived with her for 'almost 6 months', so be sure to have good records to prove your case.