Problems connecting differential ADC to SPI chain
You're misunderstanding how SPI works.

In an SPI bus every device connects to MISO, MOSI and SCK (or as many of those as there are on the chip) in parallel.  Each device then has its own separate CS connection.

You drive one of the CS pins LOW and you can communicate with the device it is connected to.  Drive that one HIGH, and the other one LOW, and you communicate with the other device.