What is this stratagem called when someone talks to you like you're a slow-witted kid?
There are a few terms which can be used for this.  The answer from @AlwaysConfused could describe the situation if you are actually talking to them like a child as stipulated in the title, but therapists should not sound patronising or condescending so I wonder if you may be referring to a form of "circumnavigation".

The use of circumnavigation may not necessarily be a case of being sly. Therapists may do this to build a complete picture of a situation as you suggest, but it can also get their client to look at things from a different angle too.

Maybe looking directly at the situation is going to be too psychologically painful right now so circumnavigating the direct path can help.

Other than this, when a therapist "wants to fish out certain information from you", there can be certain protocols which need to be followed, for example, if therapy is being given due to a situation which may lead to a court case.

A therapist in this situation cannot be seen to be leading a potential witness in a court case, so they must ask open and indirect questions.

Again, this can be see as circumnavigation of a sort, but it is more a case of open and indirect questioning.