Palpatine was just telepathically communing with Kylo under the guises of Snoke and Vader at times, to keep goading him towards the dark side -- but there is no indication that he was fully in command of Snoke's every action or whathaveyou. Snoke seemed to be a fully independent being who was created by Palpatine, and subservient to him.
Palpatine's clone 'son' was fully sentient, went on to meet a nice young lady, conceive Rey, and keep her hidden from Palpatine for years. So it was definitely possible for Palpatine's clones/creations to have wills of their own.