@bluelady
How I loathe this 'our little family, and the 3 of us' bollocks.
How rude.
You sound very angry about something. Has the OP hit a raw nerve? Do you have a family member who doesn't want YOU at certain celebrations? That's hardly surprising if you are as rude to them. The OP is quite entitled to want JUST her and her husband and baby celebrating on the baby's birthday.
How I LOATHE entitled twonks who think they have a right to see anyone they want WHEN they want. It's not a right to see your grandchild on his/her birthday, it's a privilege. It's hard enough for young parents as it is, without sniffy, demanding, precious grandparents being arsey with them.
@teachesofpeaches
Is this an extension of the MN ban on family not being able to see a newborn for a month so parents can 'bond'.
AGAIN, entirely up to the parents. Although that sounds like a load of parp, as no-one I have ever KNOWN has refused to allow visitors for a MONTH after their baby is born! 
@TomHardysNextWife
YABU. I've enjoyed my grandchildrens birthdays every part as much as those of my own children. I've made their cakes as DD doesn't like baking, and it's been a massive day for ALL the family.
Have you thought for a second that your children may want the day to themselves with their kids? Or are you too wrapped up in making it a MASSIVE DAY FOR THE WHOLE FAMILY?! 
It takes a village to raise a child.
And how i LOATHE that bloody saying. Outdated bollocks, trawled out by people who think they have a right to chip in their twopenceworth every five minutes, when it comes to other people raising their kids.
As has been said, there is nothing wrong with the grandparents just seeing the grandkid for an hour or 2, then letting the OP and her partner/DH have the rest of the day with THEIR LITTLE FAMILY!
As you were! 