Your first problem is your choice of power supplies. Because your opamps are run single-supply, they cannot provide a negative output when called for. For instance, if the input is positive, your inverter section must put out a negative voltage. Obviously it can't do that, and in fact what you see on your bottom trace is the classic behavior of a single-supply opamp being driven to the wrong polarity - phase reversal.
Second, I suspect that your simulator opamps are not rail-to-rail. This is why your outputs don't get near 5 volts.
Try this: most importantly, change your display horizontal scale to give you only 3 or 4 cycles of your signal. As presented, your data is really hard to see.
Second, instead of grounding your opamp V-, add a negative voltage source. Make both sources 15 volts instead of 5. This will allow you to see the qualitative behavior of the bridge.
Third, experiment with adding a resistor from the top of R1 to V+, and find a value (analysis will help here - hint, consider the effects of R2 and R8) that causes the DC level to reach 7.5 volts. At this point, U1 is pegged positive and U2 is pegged negative. No worries.
Fourth, use a resistive divider to bring the noninverting input of U2 from ground to 7.5, and you will see the inverter output become well-behaved. Likewise, connect the currently-grounded end of R4 to this divider, and U1 will start working properly.
Fifth, you can now figure out why the amplitude is slightly low, and adjust the gains accordingly. (hint - think about step 3 and the impedance of C1)
Sixth, reduce the voltage sources to 10 volts, then 5. Not knowing what opanps you have specified, I can't predict exactly what will happen, but it probably won't be good, especially at 5 volts. This says that you will need to find a replacement which can operate rail-to-rail.
If the circuit works fine at this point, you can check that all of the voltages are always above 0. If that is true, and only if that is true, you can eliminate your V- source.