Well, there are 2 yrs and 1 day between my sister and I. Our birthdays were always celebrated on the proper day (by which I mean family present unwrapping; parties were often on neither birthday). Am not sure why you would move one a week early - unless perhaps you're worried about being in labour on DD1's birthday this year.
Yes, we had shared parties for a portion of our childhood - primary age IIRC, certainly not at senior school - and I remember that being fine. The only problem I had was having to budge my cards along the mantelpiece in order to make room for my sister's the next day. Her major problem, I think, was, due to the fact that a couple of aunts would often get us the same thing, or nearly so, she would generally know what a couple of her presents were before she opened them. She'd ask me not to show her or tell her what they were.
And I have sort of repeated the cycle as my DC have 2 years and 10 days between them. They are not yet at the birthday party stage yet so I have no idea whether they'll share them. I am still getting my head round the idea that I'm going to have to hold kids' birthday parties full stop
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Chances are, there will be more than a day between your DCs - it's something like just 5% of babies who arrive on their due date, isn't it? - so I wouldn't worry too much. But, if they do share a birthday, or nearly so, I still wouldn't worry. As long as you treat it in a matter-of-fact way, they will be just fine.