Character recognition neural net topology/design
Your design makes some sense, but there is no need to limit connections even if you expect to represent probabilities of upper/lower case separately, because they will interact usefully. E.g if the character could most likely be one of o, O, Q, G then this might be useful information to choose the correct one. 

If you went ahead, you would need to train this network without the final layer (so that it learns the representations you expect, not some other group of 52 features), then add the final layer later, with no need for special connection rules, just use existing ones. Initially you would training the new layer separately from the full output of the 52-class net i.e. probability values, not selected class. Then you would combine with the existing net and fine-tune the result by running a few more epochs with a low learning rate on the final model.

That all seems quite complex, and IMO unlikely to gain you much accuracy (although I am guessing, it could be great - so if you have time to explore ideas, you could still try). Personally I would not take your hidden layer idea further. The full 52-class version with simple logic to combine results is I think simpler. This is also not necessary, the neural net can learn to have two different-looking images be in the same class quite easily, provided you supply examples of them in training. However, it may give you useful insights into categorisation failures in training or testing.

It is not clear from the question, but if you are not already using convolutional neural network for lower layers, then you should do so. This will make the largest impact on your results by far.