A few points. Firstly, either she is your wife, or she is your partner. Putting the word wife in inverted commas makes it - and you - sound very sarcastic and condescending, as if you are trying to minimise her status. If that attitude towards her is coming across when you are in front of the Sheriff, then I am not surprised that she is taking that as confirmation of the domestic violence allegation.
Putting the words domestic assault in inverted commas also sounds like trying to minimise what it was. The bottom line is that, if you hurt your wife, you did commit a domestic assault. You need to admit this and take responsibility for what you did. That is what a grown-up does. Saying 'but she started it, she hit me first' is what children in the playground do - and we don't accept that sort of justification for violence from our children - why should we accept it from our husbands/partners/wives?
Secondly, as others have said, I think you need to accept that you DID have a choice, in that situation - you could have walked away, you didn't have to respond to her. You were in no major danger at the time - she wasn't brandishing a knife or any sort if blunt object or weapon - it doesn't sound as if you were in any imminent danger of harm.
That said, I do think that throwing an object at a person is also a violent act, so I do think your wife also needs to take responsibility for her actions too - and both of you need to realise that if either one or both parents don't learn to control their temper, sooner or later the children will pick up on that, and will learn that behaviour too.
You are coming over very badly indeed on here - using sexist terms of abuse, minimising your behaviour, responding quite angrily to what people are saying - is this how you come over in real life? If so, could that be a factor in why the Sheriff has come to the decisions she has.
What advice has your solicitor given you? Is there a date set for a review of the access arrangements? Is there anything you could do that would show that you are trying to work on your anger management issues - a course, perhaps. And maybe a parenting course too.
And I know you are thinking "Why should I have to do courses to prove things - she started it, and why should I have to try to make myself look good for that bitch of a Sheriff - I have all this proof that I am a good person and a safe father??" - and I would answer by saying, you should do whatever you can do, to improve your chances of more access to your children - because you can either say "I don't want to do X, Y or Z - why should I?" Or you can put your own ego aside, in favour of making yourself the best father you can be for your children's sake, and giving yourself the best chance of having access to them.
First step - admit that you lost your temper, and were violent. No more excuses or justifications. Do you want your children to grow up thinking it is OK for a man to behave like that? Do you want your son to get physically violent with the women in his life, when he is older? Do you want your daughter to accept that sort of treatment from a man, because she has seen her dad do that sort of thing to her mum?