From my reading of this you messed about for a couple of years and got the final written warning (probably after a couple of lesser warnings)
You then needed some time off to care for others, was this taken as sick/annual or special i.e. unpaid leave? (suspecting you just went self certified sick)
More actual illness followed which you took sick leave for by which time the company decided to dismiss you invoking the final written warning which presumably stayed in force for twelve months.
If I were taking your case my honest opinion would be try a plea on compassionate grounds, but think you will be lucky to keep your job. Appears they may have followed the disciplinary procedure correctly and the grounds for unfair dismissal seem somewhat tenuous.
Many times I have represented people who have just been foolish and treated work as they would school. Employers do take liberties and if they haven’t followed due process are easily dealt with, but you appear to have acted in a very cavalier fashion and are probably fighting a lost cause now.