Parties in my area tend to be big and DD is only 18 months so take my input with that in mind. :)
First, I would not bat an eye at one family bringing one gift. For DD's first b-day we invited entire families and she received one gift per family, even if there were multiple children in the family.
For as long as DD is young enough that parents NEED to stay at the party, I would feed them. Simple snacks is sufficient.
Once DD gets old enough to really choose who attends her party, the invitations will be addressed only to the invited child. It is a great idea to note on the invite what the child will be doing so the parents are clued in to the fact that activities are planned for the invited guests only.
Reality is that some people don't know that only those to whom the invited is addressed are invited (we see this ALL the time at weddings!), so I'm hopeful I'll be able to roll with it if siblings show up. And, hey, if the sibling is older then I'll enlist their help ;)...which is exactly what I did at DD's first b-day!
I think you are right to want your guests to be happy! But do so within the limits of what you can manage. Beyond that it is as much their responsibility to be a good guest :)
catsandhorses is an American living in Ireland and riding mostly XC with "Bob". She is looking forward to buying a new horse when she returns to the U.S. in January'2012!