1000s of likes is not going to help your organic rankings or your Google Places/+ rankings in the 7 pack. I would definitely take 2 prong approach. Work on getting the G+ page to show up in the 7 packs for targeted local search phrases and then getting their site to rank organically for the rest.
Unless you're using Majestic, Open Site Explorer, or some other decent backlink analysis tool (preferably several of them together), you can't really tell whether your parents competitors have backlinks or not. If you're using the LINK operator for this then you should know it is VERY unreliable. It often shows no backlinks when a site might have hundreds.