Your instincts are correct - repeating the top and bottom navigation and furniture is going to be messy and confusing to the user.
If it's feasible, you could break your embed code chunks into task-specific functions so that instead of embedding your entire app, the embedding app could link to each function directly. You could have a "payments" embed code and a "services" embed code, etc. That would let the embedding app control how they'd like tasks in their navigation.
If that's not feasible, you'll want to make an "embedding-only" version of your app that strips the navigation down to the basic functions of your app. You'll remove everything that doesn't fit into a white label experience, such as having the user configure their profile in your app.
In that case, you might, for example, provide a menu of buttons to let the user navigate to each task vs. using a hamburger menu, which could conflict with a hamburger in the embedding app. When the user drills into a task, make sure the navigation they use to get around is specific to the task. For example, you might use a "Back to Payments" link button instead of a generic glyph of a chevron.
This is a project where research would be very helpful in informing your design. If you don't have them already, see if you can get 5-10 examples of existing navigation in customers' apps, and try to design with it.