The short answer is no, the PC cannot dictate to the Community Group. The most it can do (and then only if a majority of councillors agree) is to make a request. The PC can, of course, decide to withdraw its grant, although it would appear perverse for it to do so in this case.
The Community Group needs to avoid being controlled by the PC if it is to remain eligible for grants from most sources. This requirement for separation can be frustrating, but it does exist. That might be a factor in your decision to seek to become PC Chair.
Only you can decide whether to stand. It can be better for someone who is very active to avoid being Chair, as ideally the Chair should avoid pushing their views too strongly. But it does depend on what candidates are available and what you think will be best for the parish.