Hi As John notes, any grant to the charity will be on the understanding that the charity says what it is for, and then provides evidence as to what it has been spent on. However, the council needs to write to the charity and ask for that information, backed up with whatever agreement it put in place when handing over the money.
Hence, your resolution would be that the council write to the charity asking for this information (tho it should be doing this anyway). I am not sure how councillors could (morally if not legally) vote such a grant through without a requirement as to complete transparency as to how it was spent.
Re the councillor being the chair of the charity, they hold no more power than the other trustees, indeed there is no need for the charity to appoint one, other than when required to chair meetings.
Re the charity resolution to remove the power for council to appoint 'councillor trustees', the charity commission expect the council to be consulted prior to such a change if possible. If not then the council needs to raise a complaint with the charity, and if that fails, then to complain to the charity commission.