You know you don't have to tell them that you're private paying for outside SDI. But it's true that they would need a signature from you declining services, if you choose not to have the in-school SDI. So if you wanted it to stay on the IEP, you would pretty much have to let her attend the in-school SDI, and then tutor outside of school hours.
All-or-nothing is not actually legal. You are allowed to decline or accept each service or accommodation individually, as long as the accepted plan still has SDI on it (if there's no SDI left, then it's not an IEP). The district is required only to propose services that can defensibly be said to address all of the identified disability needs. As I said, if you decline services, they are off the hook. The hangup is that if you don't have an active IEP to begin with, you may have fewer rights in some states to negotiate partial rejection of the IEP. I think it's wise to consult legal advice with current knowledge of your specific state and district.
