Shazam,
I started to draw the schematic in EAGLE format. I have modified a little your original schematic because i thought R21 (1Ohm) and the 10K resistor are not needed. Maybe should we keep R21 for current limiting purposes in the switching process, but i think thats not an issue.
Circuit diagram is in the image below. It’s also necessary to reduce the charging current a little in order to reserve some of the USB current to power the DSO Nano.
The MCP73831 has a pin to indicate if battery charging is complete. So maybe it can be used to report charging status in screen (only one digital pin needed).
Slimfish
Battery - EAGLE 5.7.zip (29.7 KB)