It's fairly common for children who stutter to also exhibit another communication issue—especially speech sound disorders. When that happens, however, it's not always clear in what order the different conditions should be addressed.
The basic answer is that it will depend upon the individual student. There is no blanket recommendation (stuttering first or articulation first) that would apply to all children.
The first question I ask is, "which condition is affecting the child's communication the most?" If the child is experiencing greater adverse impact due to the stuttering, then I want to be working on that first. If the adverse impact the child is experiencing from stuttering is minimal compared to the impact from the articulation, then I'd want to work on the articulation first.
This is especially a consideration for school-age children. By the time a child reaches the school-age years, he is likely to be the recipient of negative comments from other kids about his speech sound errors, just as he might experience negative reactions to his stuttering. Therefore, I don’t automatically direct my therapy toward stuttering because that’s where my interest is; I think about what is causing the greatest impact for the child and focus my attention there, at least initially.
Of course, for most children, it is likely that they will be experiencing some negative impact from both the stuttering and the articulation errors. In that case—provided the child can handle it—it is perfectly fine (and, indeed, appropriate) to address both conditions simultaneously.
Depending upon other factors affecting the child, this may be relatively straightforward to do: As you are working on the stuttering, you can simply use stimulus items that address the articulation. This is true for work on education about speaking and stuttering, desensitization strategies, stuttering modification strategies, and even fluency enhancing strategies.
One caution that I would offer, though: you don't want the child to be working so hard on his articulation accuracy that it negatively impacts his fluency. Some children end up trying so hard to get their sounds right that they end up becoming overly concerned about their fluency. This can actually lead to an increase in stuttering severity.
So, make sure that you address the articulation in the context of good communication attitudes toward stuttering. That's the key to integrating stuttering therapy with therapy for other conditions. It can be done, but it shouldn't be traditional drill-based articulation therapy—that may well head the child in the wrong direction.
Instead, provide comprehensive therapy that focuses on helping the child communicate clearly and effectively. Maintain a core emphasis on acceptance of stuttering even while the child is learning to make modifications to his speech production. In that way, he can improve his fluency, his speech sounds, and his overall attitudes toward communication.
