Bottom of the list!

Six hours is too much in a day, but I would do as biglouis suggests and have a stop over somewhere. Somewhere you have always fancied seeing maybe?
Turn the opportunity into a positive.

I agree that a 6 hour journey is a long way to drive on your own. I know public transport can be expensive, but have you checked out the cost of National Express coaches? They are usually far cheaper than the train, and I've always had good experiences using them, particularly when travelling alone. I always make sure I have a nice coffee, water and something to eat for the journey, as well as a good book to read, or an audible book to listen to, and the time soon passes!

Meeting your cousin again obviously means a lot to you, so if your husband isn't willing to join you, I'd take the opportunity to go alone and enjoy the family reunion.

Could you not break your journey at a hotel overnight midway so you are not driving too long? It would be a shame to miss this opportunity.