Wow, I wish I had the same family as far as 'eat, don't talk, leave'... my problem is they don't eat (leaving me with gazillions of leftovers, I don't even bother anymore), they talk too much, and NEVER leave ;)
Because it's your sons first birthday, I wouldn't feel bad asking them back to your house. Keep it super simple... cake and presents... sing happy birthday, open the gifts, then BUH-BYE. Besides, your one year old won't be able to handle more than that anyway, he'd go into sensory overload ;)
My son turns 1, 4 days before Christmas (great timing kiddo)... then my mothers birthday is 4 days AFTER Christmas. I'm doing cupcakes and presents on his actual bday, then I have to see my family Christmas Eve, then I have to go BACK 4 days after xmas for mom, then the very next day my baby brother is coming back from Morocco. More family than I can handle. Hopefully, after that, I won't have to see anyone until my birthday in the middle of January. I love my family, in very, very small doses ;)