I had something similar, she gave up her claim so I could have it, I got it and then I received a letter from HMRC saying that she wanted it back.
I had to write a letter of evidence so every case will be different, but if necessary I would explain why you had them less in that period and how it is going to be in the future. Also include the children's living arrangements,such as do they have their own room at yours and hers? Include things you do for your children such as doctors, dentists, runs to
school and homework. Have you taken the children on holidays or has your partner? Who pays for clothes, food etc. Give as accurate picture of the situation to HMRC as possible. I also submitted a spreadsheet going back six months detailing every single day I had my daughter, and all the meals I provided for her during that time, and worked out I had her a bit more (due to her having some fancy holidays with the new man while I was looking after our daughter ). I would start keeping a diary of your
contact if you have not done already as this could be useful in the future.
Ultimately if you are both providing 50/50 support and care and paying out equally then you should get half each, with one person agreeing to give the other half and should be agreed between you, but understand this is not easy.
I did win my case as a dad so was absolutely delighted but be prepared to spend a bit of time writing your appeal
as was worth it in the end.
Hope that helps, PM me if you need any other advice on this.