RF switch acting like a splitter
One thing that I notice is that in the Evaluation board diagram all inputs and outputs are AC coupled:



Your schematic has AC coupling at only one of the RF switches' inputs but not at the inputs of the other RF switch and nowhere on the outputs.

It isn't clear to me if this will disturb the switching behavior of the RF switches but there is a large chance that it will. What you could do is measure the DC voltages at the outputs of the switches with and without the baluns present and with and without one of the switches present.

In your design the outputs of the two RF switches are in parallel. If the design relies on a certain DC voltage (which is set by the chip itself) to be present at the outputs but you overrule that voltage then the RF switches might not work as expected.

So: add AC coupling directly at the outputs of the RF switches and see if that helps.