I'll try again:
Your friend needs to speak to the WFTC people and ask:
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If my partner moves in will that affect my WFTC even if he is paying £X X% of his income to his ex wifes mortgage/rent etc... ?
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If so will I get any WFTC ? And how much ?
Your friends partner needs to speak to CSA and ask?
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How much child maintenance am I due to pay? I will be helping to support the child of my partner.
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Will the fact that I am still married and paying for mortgage and rent be taken into account? If yes, will there still be any child maintenance to pay? If not, how much child maintenance will I pay?
Then your friend needs to do her sums and work out whether she will miss out financially. It looks like she would.