I do think it depends on where it is .. DS1's first birthday was at a park .. so it was softdrinks all round ... we had a gathering for his sixth birthday on the weekend .. and all adults had a glass of wine (or beer etc) .. because it was at my mum's house - so its standard at a bbq at that house to do so ..
having said that - it was one glass with a meal .. for enjoyment, rather than to get ****ed .. so its a big difference.
I think the big issue here LH is that there are people in your family who do have alcohol issues, and its poor taste to combine drunken behaviour with a kids party .. so I would just distribute the invitations with the phrase " thank you for coming to our party, softdrink, juice and food will be provided - please note that as this is a child's party, we would prefer it if no alcohol was consumed" ???