How can I insert data into two different tables with a single request?

That depends on your use case, if you are planning to update them through API then you can make a new service that will execute simultaneously two queries in two different models.

But if you are looking to achieve this from the Strapi’s Content manager than you should take a look at the lifecycles hooks (afterCreate, afterUpdate).

I’m still not getting the point for copying the same data in two different places, unless you copy it conditionally? But anyway you can filter data and there is no longer need for duplicating it over two models. Can you explain your use case?