I've just put together a long and very funny post about the client who has decided that she doesn't need my assistance any more, and sadly concluded that it's much too identifiable and can't be posted BUT...
If you tell an external contractor that you're going to take their job in-house because you need somebody who will be available at all times, then making the job part-time and giving it to somebody who is available even less time than the external contractor isn't going to work.
Also, it might be a good idea to get the contractor's Monthly To Do List and review it as part of the hiring process. The New Hire probably needs to know what's on it, and the conversation that starts 'I didn't know you did that!' makes the CEO look foolish.
When you have to call the Contractor to pick up the pieces because New Hire has done only part of the Monthly To Do list and then gone on leave over the deadline, a please and a thank you go a long way. The contractor is already planning that when the actual contract runs out (11 days. 11 more days) any subsequent hauling you out of a pit of your own digging will be at Consultant Rate, which is Contractor Rate plus one third. Taking up all of the contractor's free time for 5 working days is probably not unreasonable, but it would be more palatable with a thank you.
Taking half the weekend because New Hire has messed up the small bit of the work they actually completed, and it all has to be undone and redone, definitely warrants acknowledgement. Consultant Rate is touching Contractor Rate and a half. Saying, on Saturday night, in an email copied to 6 people, 'if we want you to work through Sunday as well, we'll tell you,' without adding any appreciation of Contractor having gone above and beyond, causes the Consultant Rate for future rescues to reach double Contractor Rate.
When you have told the Contractor that all current work belongs to the New Hire, you should not be surprised when email queries to the Contractor receive the answer 'ask New Hire'. It is not the Contractor's problem that the days you have arranged for New Hire to work are not the days on which the work actually occurs.