hiya
sounds highly dodgy to me, if you were the only one!
I would think you do have a decent case of success at tribunal and if you are getting legal advice they will help you with presenting it properly and keeping records of everything etc
However, tbh you will probably be best to settle it. Actually going to tribunal is extremely stressful, time-consuming and can take a long time to go through the whole thing. Thinking about your personal situation you don't need that!
I would suggest in your position you would be better to negotiate the best possible settlement for you. You don't need to settle for a crappy amount for something like this -they are hoping you will take it as it's the easy option, and will go away quietly!
Getting a better settlement may involve proceeding as if you have every intention of going to tribunal to 'bluff' them to go as high as possible. Believe me they won't want to end up in a tribunal, it will be cheaper and easier for them to settle, but you can ensure you get the best possible settlement by pushing them all the way.
I would refuse their offer, write (get your legal adviser to write if poss) refusing it, stating you feel you would have an excellent chance of success at a tribunal, so would rather proceed along that route, as compensation you would receive would be much higher than their offer.
Something along those lines.
They should come back with a higher amount if they know what's good for them!
let us know how you get on