EIC

Hi, parents married living apart for 3 years.. they each claim 1 child each that they have together. i ask them how many months out of the year the child lives with them and they tell me 50/50.. i wasnt sure if i can do the person with the lowest income claim 1 kid fully to get HOH, and then claim 2nd child to increase her EIC.. the dad claims his parents so he is already HOH..but due to income being high all he gets its CTC of 2,000...can they determine who is custodial parent? so that way i can have the dad sign off the eic/hoh credits over to the lower income mom? i dont want to make any errors or do something wrong I want to do it right in the yes of the IRS and most beneficial for my client. What are your thoughts? Does anyone have a worksheet for a #of nights checklist lol or anything i can give my client to fill out to help them determine who had the child the longest when they say 50/50? 

Edit: I got my answer. Tie breaker rules dont apply here due to residency not being greater than 51 days or or more so since its equal days spent then i have to follow the rule that the person with the highest AGI must claim the child" I just get confused when reading it says "in most cases" so i wonder what the not most cases are and that is when i question..but i see it more clear now. Thank you everyone!