Separated: Child Tax Credits

My ex and I split when my daughter(now 7) was 10 months old.
We have shared contact/residency 50/50 since then.
I have my daughter for 3 nights during school week(Fri/Sat/Sun) and more over holidays.
I earn approx £ 17.500 p.a ,my ex , who doesn't work, has always taken the whole of the credits/benefit.
We have been in mediation before which really helped with contact issues but for the past year,my ex has not wanted to attend a mediation session to discuss a fairer share of the credits/benefits saying she has no money.

My ex who has been in rented accommodation and receiving housing benefit has always claimed she needed the money due to not working.
Now,however, she has just bought an £180,000 house and is spending another £20,000 (at least) getting it done up. The money was from an inheritance from her Grandfather but had always been kept under an account of her parent's.
In addition,I know my ex has been doing cash in hand jobs and receives a £5000/year "Director's Loan" (from a company her new boyfriend owns).
I spend a lot of money on my daughter: clothes,haircuts,cinema,theatre,days out etc.. none of it begrudged
but her mum spends very little in comparison.

What would people recommend as a next step?
Thanks in advance

You need to bear in mind that you can't share CB or child tax credits.

Only one of you can apply.

You have to decide which of you it will be.