I hate the go against the grain here, but I can see a tiny shred of credibility in her predicament.
Namely, I don't think the six year old knew about sex yet. To explain why a woman can marry a woman, you have to explain that they cannot reproduce. To explain why that is bad, you have to get into the details of what heterosexuality is down to the dirty details.
While it is up to the discretion of the parent to determine what is the appropriate age to discuss what sex is, I personally don't think a six year old should know about that kind of stuff yet.
Though, I don't see why this merits the game of Life being turned into a conservative controversy. It's not like the game is encouraging players to be gay (i.e. giving bonuses or abilities only to gay couples) it merely just gives players the option to. I think the mother kind of aggravated the situation when her daughter had questions. She could have took the low road while maintaining her position and said "What? I don't know why you are able to marry other women. It's probably just a mistake, you should only marry men." No, she just had to interject her opinion when she was presented with conflicting viewpoints. It's very common trait for christian people to get preachy and soapbox a lecture whenever issues of sin and immorality present themselves. As long as any form of media or physical existence of anything that is not wholesome, biblical, or can be interpreted (however far fetched) as non-biblical, Christians will oppose it with extreme gusto. Do you remember the Christian witch hunts after Pokemon, Harry Potter, The Da Vinci Code, and most forms of secular music? It's a fact of life that this religion is notorious for picking fights with anyone or anything that doesn't fit into their idea of a godly lifestyle. They do this because in their world, when they see non-christian anything they see it as a personal attack on their beliefs and the well being of their children.
Sorry if I'm stating the obvious here, but I felt it needed to be said.