How do I put these two into a single mesh?

I think I went through all the mesh commands, but does anyone know how to make these two into a single shape? (the bottom of the circle medallion will be closed up, I just left it open for now)
floral_button1.3dm (6.8 MB)

Hi Izabela
This mesh model has several problems with the leaves. There are parts that intersect (you need to create _ungroup to see it well). There are holes and geometries that intersect. When I repair these types of meshes, using Rhino involves a (too) very long job. I don’t write an English good enough to explain the process here, because it’s long and quite complex but I want to suggest not using Rhino for these things (I apologize to McNeel). Better to use suitable mesh repair programs (for example on Mac you can use Meshmixer) Since I am unable to explain, I attach the file entirely worked with Rhino 5. Solving the problem by providing the file should not be the way to proceed …

floral button Rhino 5.3dm (16.6 MB) ![18|690x431]

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I see. Thank you so much for your input. I will look into the program you mentioned.