I’m not convinced that dying would look very good. It would probably be easier to simply get some new curtains made in a fabric that you like. If you are handy with a sewing machine you could make a set in a few hours using the original curtains as a template or alternatively, any curtain maker would make you some if you provide them with the fabric you want and the old curtains to use as a template.
We live in Liverpool and there is a fantastic shop that sells curtain fabric all at £4.99 per metre and they have people who make up the curtains for you if you don’t want to do it yourself. I see you are based in Cheshire so a day trip to Liverpool might be in order or I am sure your local town will have something similar.
I did this and it wasn't overly successful. They were the standard beige type colour and I chose a dark green but they came out a weird speckly camouflage type shade. Still used them but the fibres weren't the right kind to be dyed.
Another thing that has just come to mind is that there is a strong possibility that the caravan curtains have been treated with a flame retardant. I’m not sure what the law says about this or what manufacturers do, but if this is the case, there is no way fabric treated with flame retardant will dye in an attractive manner and might explain the weird effect that happened in the previous post.