The issue of guest's dates is a tricky one. Many single people look forward to bringing a date to a wedding, but for the bride and groom that means having a stranger at a very personal event. With limited budgets, that stranger is quite literally taking the place of someone they do know. My advice is to create a blanket rule, and do your best to stick to it. Such a rule might be "only couples that live together." So, you might never have met your coworker's husband, but under that rule, he would be invited. Or, "only couples that have dated two years or more." You could even go so far as to say, "couples that are in relationships are okay, but we certainly don't want any first dates, or friend dates."
Do try to be generous if you can, particularly if the majority of your guests are older. Older guests often feel less comfortable dancing by themselves, or mingling. You want your friends and loved ones to be able to relax and enjoy themselves. This article from the New York Times does a good job of explaining the stick.
In the case of my reader above, I do think you need to invite the nephew's girlfriend. Two years is a serious relationship.
What do you think, readers?