I'm going to focus on energy and carbon emissions because that's what I know best. Anyone wanting to add waste generation and other considerations please feel free.
Chad is right that the question depends first on how your kids live and where you decide to live. Geography and economy are very important variables. A study by Chris Jones at UC Berkeley broke the average carbon footprints of the US and world as follows:
Science Daily has the total figures as 20 and 4 tons for the US and world respectively. I suggest this has to do with Jones accounting of indirect supply chain emissions he calculated using lifecycle input output analysis, so I tend to trust his figures.
A paper Jones published in Environmental Science and Technology showed, using the same methodologies, that these distributions can vary substantially. For instance, a comparison of San Francisco vs St. Louis showed the following differences:
- transportation emissions 2x as high in SF compared to SL
- housing emissions over 2x as high in SL compared to SF
- food emissions twice as high in SL compared to SF
- goods emissions ~30% higher in SF compared to SL
- service emissions ~40% higher in SF compared to SL
Because I'm not sure which locations you are choosing between, I can't say what categories will be most important to you, so I'll use the average US case. Based on Jones' analysis we see that transportation, electricity and heating are good place to start to look at reducing your carbon impact. The first consideration you should therefore make is your traveling habits at the two different places:
- As a retired person will you be traveling on vacation a lot? Using
EPA Climate Leaders' figures, we can crudely estimate that a 6000 mi flight * .185 kg / passenger-mi results in over one metric ton of direct CO2 emissions — roughly 10% of the average American's direct transportation emissions — not insignificant.
- What will your daily commute look like? If you're staying at home wiping the grand kids' ass then score some points for sustainability! However, if you are going to need to drive your car for entertainment, volunteering, work in either situation, you'll need to exploit opportunities to carpool or use a low emission vehicle (think electric with solar).
- What will the building situation look like? If you can't directly compare electric and heating bills, consider the natural lighting, the climate (a more extreme climate leads to increased HVAC loads), insulation and air leakiness of the house.
Now more specific to your question, let's hold these factors constant and just consider how adding an additional person to a house can contribute to sustainability. Every four years the EIA conducts a residential energy consumer survey. Now here is some data I love and think would be very interesting to you (there is a bunch of other great stuff in there for any data junkies):
There are substantial energy savings from increasing the number of members per household. However there are diminishing returns to adding another member to the house. So the first person would contribute 30% per capita energy savings, the second 20%, the third 10%. This is important from a macro-perspective. Let's say you have 30 people and developers are considering design occupancy. The improvement from going from six 5-person units to five 6-person units is not as significant as moving from fifteen 2-person units to ten 3-person units.
From your perspective as an individual (or couple), there will be significant advantages to living in 5+ person house compared to a house for one or two people. Let's say you are considering a two person house vs a six person house. Moving into the two person house, you would be responsible for 50% of the 2-person house's primary energy (45 MBtu). If you were the sixth person in a five person house, you would be responsible for 4MBtu margin of going from 5 person to six person house. A huge difference! These gains are mostly from shared energy sources, such as a refrigerator, shared lighting, shared air temperature etc.
Obviously energy consumption is very different outside US, but the principles should hold.