How to solve a a full wave rectifier with two diodes and a ground in the middle?
Two things I recommend when you have confusion with these puzzle pieces.

1: Break down the circuit into two, one showing current flow during the positive phase, the other during the negative phase.  

This allows you to ignore "what the other diode is doing"- you don't care because it's an ideal diode in this exercise, so when reverse biased that means that current through it is __.

2: The other aspect of these puzzle problems is the way the schematic is drawn- nominally in a bridge configuration, but sometime that makes it difficult to see how the components are interconnected.  Redrawing it in a rectilinear fashion sometimes helps.

Note that ground is a relative term.  Sometimes it's convenient to call some  node "ground", but that doesn't make its voltage automatically equal to some voltage source, which is ultimately the reference source in this circuit.