Hi There!
I think you have a coupple of choices. One would be to limit the people that is coming to 6 or 7 of kids his age and have a 1 to 2 hours max party for them, just for one year olds, That's really all they can take at that age without getting fussy or crancky.
OR (I don't know where you live but this is easy), if you really can't or wouldn't like to keep people out of the celebration there are plenty of parks (playgrounds),with pavillions that are just there for people to use without reserving them, kind of first come,first serve basis. That way it doesn't cost you anything or a very small fee in some cases),and there is PLENTY of room for everybody to run arround. Now somebody has to be there early enough to reserve a spot (husband are great for that job!)
A.