Oo er! That does not look particularly robust yarn just from the pic. I don’t think the company should be stating that you need to knit “gently” with the yarn either, because the tension of the knitting is determined by the pattern, and if you knit too loosely it will loose its shape and leave you requiring a lot more yarn than is stated. I haven’t got any experience with Ice yarns but I have knitted with lots of different yarns, both cheap acrylic and much softer and more expensive types and never had any trouble with breakage.
From my beadweaving I also know a bit about thread of all types. All thread except the very strong nylon fishing line sort is made from shorter fibres spun together. The force that keeps the fibres from separating and pulling apart is mere friction, but don’t worry-friction can be very, very effective (think of velcro) in forming a strong bond that will last years. All the fibres listed are suitable for yarn. If you imagine traditional spinning, the yarn is first spun into a single ply thread and then that thread is spun back on itself to produce a two ply yarn. If the initial thread is not spun tightly enough then there is not enough friction to hold the fibres together and you end up with the same result.
I think you are well within your rights to ask for another batch of wool. You need to make sure you have all your balls of yarn replaced because they need to be matched and dye colours can sometimes vary between batches, leaving you with obvious blocks of colours that are slightly different.
There are some spinners on Folksy who might be able to give you more insight into the process.
From a legal perspective, any product sold to a consumer has to be “fit for purpose.” If you can’t knit with it, then the company does not have a leg to stand on.