I really feel for you. You must feel very shocked and scared.
My ex has HD in his family, but it wasn't officially diagnosed until 1990 and various "symptoms" within the family previously which, with hindsight, had probably been HD were attributed instead to various mental illnesses and alcoholism (though of course the 2 conditions aren't mutually exclusive).
His mother was the 1st in the family to be diagnosed and we were told, by a social worker, to "think hard before starting a family" ..... when I was 7 months pregnant (but wearing a big coat !). Needless to say, it was very frightening. At the time, there was no predictive test available .... I think it was introduced in 1995. Thankfully my ex is clear, meaning that my son is clear too. However, 2 out of 3 of his siblings will get it .... last I heard, I think the 3rd doesn't want to know.
His mum was diagnosed when she was in her early 50s but there had been several years past history of SS involvement, sectioning, alcoholism, disturbances with neighbours and so on .... which were almost certainly symptoms. She died I think about 2 years later, from a nasty accident, but sadly, so far as I remember, this was caused by her lack of co-ordination (and therefore vulnerability) as opposed to directly from HD, but I suppose the disease was to blame.
I hope I'm not terrifying you but it would be stupid and insulting to pretend this disease is pleasant.
If you do decide to have the test, I think you will undergo counselling beforehand .... I don't imagine they will just do it in a "matter of fact" way. I am so sorry you are having to face this ..... I can remember the 5 or so years I lived with the idea of it affecting my child and it was a gut-wrenching thing which you could forget about most of the time but which, when it popped into your thoughts, was devastating. I'm also very sorry your dad isn't prepared to have the test ..... I know it's a dreadfully scary thing to do, but if he did it, he might be able to put a stop to your anguish sooner than later, if he's not inherited the gene of course.