How can I separate and recombine yarn?
First of all, even when you can split the yarn, it will be easier to buy thinner yarn or use the yarn you have in alternate turns, mixing the colours by using them next to each other. You also control the use of colours better that way.
To test whether the yarn can be split at all, take a short length and take it apart. If the different parts split off easily you can go on and try a longer bit.
Often the yarn has fibres sticking out and getting caught in the other strand in the process of twining and winding.
To split big lengths you will need to spin the boll of yarn at the same speed as you un-twine, or it needs to be allowed to spin freely while you take it apart without putting any stress on the more delicate strands.
While you untwist and split the yarn you need to wind the two (or more) stands at the same speed and the same time.
While I am sure you can make a machine to do the work, I doubt it will be easy to buy one, I do not remember ever having seen or heard about one.
I would go with the advice my textile-crafts teacher told me back when we were weaving with colours. Do not try to work with mixed colours. Do one or two strands of one colour and then one or more of the other. Giving you the same visual mix of the colours but more control on how they work.