3rd party saying injuries could not have happened due to accident?

I was involved in an accident a few months ago. My mother was in the car with me. , 3rd party have admitted liability

Luckily I escaped with no injuries but my mother suffered what the doctor said was 'tissue damage due to the accident'. She has informed teh 3rd parties insurance she wishes to make a PI claim but the 3rd party and their insurance company are now saying they dispute the injury was caused by the accident due to the low speed of the vehicles. It was slow, but was hard enough impact to cause over Â?1000 worth of damage to my car.

My mother is quite upset about all this and has signed to say her medical history needs to be accessed. She had to have 3 weeks off work (she stands all day in her employment) and is still in mild pain ie cant lie/sit/stand for a long period of time. She does however suffer from arthitus (sp?) but hasnt suffered for a while due to being on medication for it. She says she knows the 'type' of pain the arthiritus gives her and this has been different ie shoulders which were never effected prior etc and constant back niggling since it happened.

Her concern is that the 3rd party wont pay out for time lost at work (only on ssp) and any damages ie her whilplash and backpain as she has a pre-existing condition.

Could anyone help me help to her to be a little more re-assured about the situation?  I know she is genuinely suffering as she couldnt walk for 3 weeks, starting the day after the accident (this is not due to pre existing condition as she hadnt needed to take any medication for that for months)

Can anyone tell me if she were to persue the claim would she get compensation, would it be reduced due to pre existing condition, would the 3rd party insurance want to go to court?