The tax credits thing isn't right. This is something CMS staff rarely understand, and so you often need to point them to the right info.
The relevant bit of law is Regulation 50(2) of the Child Maintenance Calculation Regulations 2012. Regulation 50 says:
"Parent treated as a non-resident parent in shared care cases
50.—(1) Where the circumstances of a case are that—
(a)an application is made by a person with care under section 4 of the 1991 Act(1); and
(b)the person named in that application as the non-resident parent of the qualifying child also provides a home for that child (in a different household from the applicant) and shares the day to day care of that child with the applicant,
the case is to be treated as a special case for the purposes of the 1991 Act.
(2) For the purposes of this special case, the person mentioned in paragraph (1)(b) is to be treated as the non-resident parent if, and only if, that person provides day to day care to a lesser extent than the applicant.
(3) Where the applicant is receiving child benefit in respect of the qualifying child the applicant is assumed, in the absence of evidence to the contrary, to be providing day to day care to a greater extent than any other person."
So, as you can see Reg 50(2) says that you are only an NRP if you provide day tp day care to a lesser extent than the applicant. In most 50/50 cases, you are providong equal shared care akd so you can't be treated as NRP. No maintenance is therefore payable.
The knly way that benefits come into tjks picture is under Reg 50(3), which creates an assumption that if you are receiving ChB them you are probably providing greater care. But that's just an assumption, that is overturned if you can show that care is equally split. Tax credits are completely irrelevant - the law doesn't care who gets TC when deciding if maintenance is payable.
So, you need to point the CMS to this regulation. They have some questions they should ask to help decide if care is equal (it's things like who deals with medical appointments etc). Assuming it is, they should then confirm that nothing is payable.