Child benefit

Hello.
I'm a father of 8yo boy. We are not together since birth. When my son turned 2yo he strongly expressed distress whenever time to bring him back to his mother came about. Fast forward,he turned 5 and he would still get upset and angry when his mother took him to spend her 50/50 with him. So then we changed to 60/40 where i would take him 4 nights and she 3 nights per week. This arrangement also made him upset so since June this year he stays with me 6 nights one week and 5 nights week 2 . So basically on week 1 she has him Monday night and week 2 Monday and Tuesday only. I spoke to lawyer if I needed court order to make this official as she is collecting benefits towards him . The lawyer said that most likely judge will not issue court order if arrangement is amicable and inline with my sons wishes. I spoke to HMRC and was told that if there is significant difference between shared parenting time she shouldn't be claiming and I should make counter claim. If there is 50/50 then they will investigate who does more in terms of doctors appointments etc. I want to succeed in my applications and not get fobbed off like they always do to men. This arrangement we have is going to be in place for quite some time. School knows he is with me 6 nights because they even put my son on SEND program due to his agressive behaviour at school prior 6 nights arrangement. My son was upset asking teachers to call me when was his mother day to pick him up so I turned up and things changed. Since June I take him as we agreed and during summer holiday or break from school like half term, jubilee etc she doesn't take him at all. Because he will not leave my house. Any advice regarding HMRC guys?