My son went to a tutor that turned out not to be good enough, so I finshed his preparartion myself.
I still wanted him to take his practice sessions seriously, so I didn't tell him that I was going to replace the tutor.
On the usual day, I let him get ready and only as we should have left home I told him that I was replacing the tutor, but that we would take the sesson just as seriously.
He was happy not to go to the tutor, and was ready for the practice session, so it went well.
So I do understand you wanting to get your son into the 11+ practice habit with a tutor. But I am also suggesting that you could let your son believe that he is going to have a tutor, and to let him discover that its you at the last minute. A bit devious I know...
Best of luck with whatever you decide.