The flow of electrons in the outer circuit during re-charging will still be from anode to cathode, while inside the cell, the flow of electrons will be from cathode to anode. Re-charging is like an electrolytic cell. The anode of the external battery is connected to the cathode which makes the cathode as -ve, and the cathode of the external circuit is connected to the anode, which makes anode as +ve. So essentially when electrons flow from anode to cathode in external circuit, inside the cell they flow from cathode to anode. I like to think of galvanic cell as charging, and electrolytic cell as re-charging. Let me know if I am wrong.
You're walking into a world of heartache and pain trying to wrap your head around the whole "which is positive and negative and why". It's a minefield. It's like trying to talk to my Uncle Donald about politics at Thanksgiving dinner after he's housed a dozen beers. All you're going to do is get angry and confused.
Just memorize: GAIN. Galvanic Anode Is Negative. That'll get you through any MCAT questions that require you to know which is pos and neg.