Typing on phone not using quote marks.
Home is a special case. Don’t use it in examples. Note how you can’t replace it with library.
I think:
Me is the subject of smile and smile is the object of make.
Me is the subject of throw and throw is the object of make. Ball is the object of throw.
In general, if it seems like the make or other verb applies to the whole group, that can work by it applying to the nonfinite verb which then governs a subject and or object.