Flip flop/latch with isolated differential input and differential output
As close as I can get to understanding what you're asking for, you might want something like this:



XFMR1 provides isolation from your inputs. If your input is actually single-ended, "IN-" will be the reference (ground) of the source circuit. If you are using single-ended instead of split supplies, you could tie the reference of the transformer secondary to a mid-supply voltage instead of to ground.

OA1 and OA2 are being used as comparators. R1, R2, and R3 should be chosen to give thresholds corresponding to the minimum positive and negative pulses you want to detect. 

LTCH1 is an SR latch that provides the latching behavior you requested. Depending on how OA1 and OA2 are powered, you might need voltage dividers or zener circuits between the comparator outputs and LTCH1 to give the correct logic levels. Or you might use comparator ICs with open-collector outputs, in which case you'd add pull-up resistors to LTCH1's supply to get the correct voltages.

OA3 is a differential op-amp, for example maybe THS4521. Feedback will need to be provided to give the output amplitude you want. Note that this op-amp will be attempting to force its common-mode output voltage (following an additional input that's not shown in my diagram). If you want a circuit that applies a differential voltage but allows its load to determine the common mode voltage, this will not work.

Final part selection of the comparators, latch, and differential op-amp will depend on the speed and repetition rate of the input signal, available power supplies, etc.