Battery charger MCP73831 (2-OT) doesn't charge LiPo battery
USB and MacBook you say...Your USB can deliver 5[V] but can it supply the needed current?
First of all, USB 2.0 can deliver at most 500[mA]. You need to supply current to both circuits, which is the battery charger and the load. Your current is split in two, 300[mA] to the charger 200[mA] to the load. I won't go into the details of how current works.
Second of all that DC-DC circuit with the transistor is redundant in my opinion and should be discarded.
EDIT:
My remark about discarding DC-DC is wrong, I was thinking about something else.