It is not unusual for a charitable organization to create a 501(c)(4) social welfare organization to loosen the restraints on lobbying and electioneering. (Some (c)(4)s likewise create (c)(3) charities to raise tax-deductible contributions for their educational or litigation activities.)  The U.S. Supreme Court has specifically sanctioned the use of dual entities to promote their goals. 

I don’t understand how the president of the charity could unilaterally create a (c)(4) that has not been approved by the board.  This sounds as though it could be a free-standing entity.  Normally one of the entities controls the other so that their activities are fully coordinated and the finances are under control.  There may be a technical conflict of interest between the officers and the boards, but when their purposes are consistent, it is easily waivable.

It would be very helpful to have written guidelines regarding the separation of duties and expenses.  The key thing to remember is that the (c)(4) can give things (like money and services) to the (c)(3), but the (c)(3) ought not to be giving things to the (c)(4).  The IRS does not like using charitable assets for non-deductible, non-charitable activities.