I'm afraid that I see no robust appeal argument here. Of course the council will never give way, they just want your money, but your wife not knowing what the signs mean is the basic reason the PCNs have been served. The PCN for the 27th is only 7 minutes within the afternoon restriction, but that is, unfortunately, not in de minimis territory.
If you have any more background info you can share with us, it could help with an appeal, for instance are you long-term London residents or quite new to London, how long has your wife been driving, etc. I hate to say pay-up without at least submitting some reps so they have to do at least some work for their money, but it's your choice. Hackney normally re-offer the discount when rejecting representations, (reps).