Welcome!
I'm approaching this from experience on the school side of the special education process, not the parent side. I would be very cautious about rejecting a portion of an IEP based on your discomfort with the qualifications of the service provider. Service providers can be changed. Rejecting the service won't force the district to get your DC a more skilled provider, it'll just remove the mandate to provide the service in any form; changing the IEP, once rejected, will be more complex. Once the school proposes a service, and you reject it, their responsibility with regard to that service is done, and you reduce your leverage for getting the service reinstated. Especially on an initial IEP, where there is no stay-put.
It's a different question, of course, if you believe that engaging with the service using this provider will be injurious, rather than simply not effective, but I would imagine you would have mentioned it if this were the more extreme case.
Depending on the service in question, the likelihood of negative outcomes to your child from waiting for service, and your access to qualified private providers, as well as how you wish to allocate resources, it would probably make the most sense simply to find an outside provider in the short-term, and try to work with the district on finding a qualified in-district provider in the mid-/long-term. If you wanted to also pursue legal recourse, in the event you won (which, as you note, is not guaranteed), the district would likely have to pay for the compensatory services that you sought outside. So you could, if you wished, take a chance that you would win, in which case you would end up paying for only the litigation. But that's not a slam dunk, of course.
