Be careful about your terminology.  Nobody “owns” a charity.  The founder may control it, but he doesn’t “own” it.  He can’t sell it.  He can’t dissolve it and take the net assets for his retirement.  Even where state nonprofit corporation laws permit the transfer of membership interests (a practice often utilized by social clubs), a state Attorney General is likely to frown on an individual member benefiting from the sale of a charitable interest to private parties.  If the IRS looked, it might revoke the exemption on the basis of private inurement to an insider.

The practical way to transfer control in a membership corporation is to admit the new member or members and then have the old members resign.  There is no change in the corporation or its structure, only a change in the identity of the people who control it.  (See Ready Reference Page: “Mergers and Acquisitions Can Take Many Forms”) You still have to be concerned about bond covenants, leases, or other contracts that might require approval from another party for a change in control, but most of your commercial and professional relationships will be unaffected by having new leadership.

If the founder wants to give control to his children to run the corporation together, there may be nothing more to do to accomplish the transfer of control.  You may not even have to amend the bylaws if they were drafted with the possibility of multiple members. 

If the founder wants his son to control the school and his daughter to control the daycare, he may want to divide the corporation into two separate corporations before the change, assuming that the state law permits divisions of nonprofits.  The kids (who I assume are not actually kids anymore) could also cause a division later if they wish.

The legal technique for making the transition is pretty simple.  The personal and emotional requirements for making the transition smooth create other issues entirely.