I would go with your instinct and cut out all of the professional services, since you don't seem to have much faith that they are helping.

Through her playdates, she's learning social skills naturally, through play with other kids. If she has challenges, you can work through these with her as they happen, with love and empathy. Plus, with the playdates, she's building REAL relationships and REAL friendships, which is the ultimate goal of building "social skills".

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The major social problems that they're dealing with are, a) accepting that peers are not judging or thinking ill of DD, b) not overwhelming peers with love and attention, and equally not expecting absolute reciprocity and fidelity in relationships, and c) not acting out of fear or social anxiety in complex and dynamic social situations.
Are those the social issues that they work on in the Thursday social skills class? If they're not working on the specific skills she needs, then I don't think it's very helpful.

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Her therapist says that she has never worked with an adult or child more clearly in-touch with her emotions and motivations than DD, and that DD seems to innately know what the correct course of action will be... but at 5 she just can't apply those skills.

Reading between the lines, it sounds like the therapist really doesn't know how to help her. As a parent, though YOU are best able to learn to apply these skills by discussing her day with her every day, praising the positives and helping her learn to reflect in a positive way. Patience and maturity will help a lot.

It takes a lot of courage to go with your instinct, but if your only reason for keeping these services is because you think the school will be less likely to work with you, I don't think that's a good reason, as these services seem to be doing more harm than good because of her lack of downtime.

If it ever comes up, I'd just tell the school that you couldn't afford the services anymore. Where I live, these sort of things cost over $100/hr and are not covered by insurance unless you have a diagnosis.