What power in outlets forces electrons to flow back to anode in batteries?
There is absolutely nothing magical about the power in an "outlet". There is simply more of it than there is in a battery.

As a simple illustration, take two rechargeable batteries - one flat and one fully charged. The flat one will have a much lower voltage than the fully charged one. Let's say they're 0.8v and 1.3v respectively.

Connect the batteries to each other in parallel: + to + and - to - (note: don't actually do this, you might overheat and blow up your batteries - just do it in your head). 

Now one battery wants the voltage between + and - to be 1.3v but the other can only manage 0.8v. So the stronger battery wins and pulls the voltage up to where it wants it to be. In order to do that it has to "help" the other battery to get there, by giving it some of its charge.

After some time both batteries will find an equilibrium where they have the same amount of charge and both want the voltage to be the same. At that point everything stops. The flat battery has gained a fair chunk of charge, and the charged battery has lost an equivalent amount of charge.

Now the difference with an outlet is purely that there is a seemingly infinite amount of charge to "help" the flat battery reach the voltage that the charger wants it to be - the charger never goes flat - so the flat batter can be "helped" all the way to full charge - and beyond if the charger doesn't know when to stop.



Note to pedants: Yes, this is all completely wrong, but it paints a picture that helps the OP understand basic concepts.