Here's
a downloadable video- change Shading to Solid to see things better;
- select the mesh and switch to Edit mode (TAB), disable Limit selection to visible, press B to activate box selection, select one earring, press Delete key and choose Faces. Do not duplicate and mirror anything until you’re done with uvs, weights and vertex paint;
- select everything with A, Shading/UVs – Clear seam;
- choose Face select, select one face on the bug, Select – Linked, press P – Selection to separate it;
- select s4studio_mesh_1.001, select one face on the front side, Select – Select similar – Normal, Select – Select More/Less – More, P- Selection;
- select s4studio_mesh_1.002, in Object mode add Triangulate modifier;
- switch to Edit mode, select everything, switch to Vertex select. Holding Ctrl-Shift, deselect small holes in the middle, Tools – Remove doubles with Merge distance set to 0,0001, Ctrl I to invert selection, remove doubles again with 0,00005;
- select one face on the front side again, press Shift 7 (the one that is on the right side of the keyboard, not the top row ), select everything, Shading/UVs – Unwrap – Project from view;
You can go about unwrapping them in two ways:
- turn on sync, switch to Vertex select, Select – Select boundary loop, Ctrl I to invert, UVs – Pin, select everything, unwrap. The front will retain its shape but the sides will overlap in some places, you can move them manually;
OR
- just select everything and unwrap. The front will lose its shape but the sides will not overlap.
- repeat on the back side;
- select s4studio_mesh_1, Shift-Alt click on some edge loops and mark them as seams, select everything, unwrap;
- straighten one face ( W - Auto align), turn off sync, select everything in 3d view, switch to Face select, select straightened face, choose Follow active quads;
- do the same for the other ring, join everything together, put in the right place
blend 
