How can I "Ladder" Mosfets to disconnect balancing lines from a series of battery cells?
What do you want is called BMS(Battery Management System). 

Basically you want to protect the battery so it can withstand among many other things: over/under current, over/under voltage. Since nowadays people are putting batteries almost everywhere, IC manufacturers responded appropriately. You will find tens of IC solutions for just the thing you need. Most popular being:


TI - BQ76PL536(Tesla's choice)
Linear Technology - LTC6804(BMW's choice)


Read the datasheet carefully and you should be able to create basic circuits. Go further, connect it with MCU capable of driving FET's as well as communicate with the IC and you will have very basic BMS structure.

However, if your budget could not afford one of the above IC, take analog multiplexer along with differential amplifier and use MCU's internal ADC for measurement. Luckily, you will have 12 bit resolution ~ 1-2mV measurement error(Li-Ion) after compensating