Disclaimer: I am not affiliated in any way with EA Games, nor am I being compensated for my efforts. I just like the game.
Note: I am going to be writing part of this "in character" and then part of it not in character. I will indicate that by differences in text color.
Quinton John Riedmayer, Jr., [in the red shirt] better known as Jack, was never interested in all that "take care of the family business, carry on the family name" nonsense. He was more interested in seeing how many girlfriends one man can have without getting sucked into marriage. He did pretty well, too, until his share of the inheritance dried up and he was forced to move in with his brother.
Elwood Riedmayer [in the green shirt] was always a little ashamed of his older brother. He tried to make up for Jack's indiscretions with his own excellent behavior. He took over the family business when he was just 18, married not long after, and obligingly did his best to father an heir. But his only child was a girl. And not just a girl, but a flighty girl interested only in parties. Elwood did his best to support her and keep her from shaming the family name, but then his wife Edith got cancer and things began to go downhill. Once she died (around the same time the family business floundered), Elwood decided it was time for a fresh start and cashed in his assets to buy property in Prosperity Plains. The only trouble is, now he needs a male heir all over again, and he's not really interested in remarriage.
Beata Riedmayer [blonde hair, colorful dress] was always closer to her mother. Her mother was the one who was home, after all, not always away on business like her father. When she gave birth to twins out of wedlock, it was her mother who supported her and helped raise the twins. When Beata became pregnant again several years later, it was her dying mother who convinced her father not to kick her out of the house to fend for herself. Now her mother is gone, though, and Beata has moved with her father to Prosperity Plains. She hopes that they can find a way to be friends.
Edith Riedmayer [dark hair, blue jacket] was named after her grandmother, but she inherited her grandfather's keen business sense. She also inherited a bit of his impatience with Beata's flightiness. Edith has high ambitions and she needs them, since it will probably be her job to keep the family afloat financially after Grandpa dies.
Joan Riedmayer [dark hair, pink shirt] doesn't like the way Mom runs things (or rather, fails to) any more than Edith does. But she thinks Edith is silly for thinking that money can solve all their problems. The most important thing is being committed to your family above everything else, no matter what.
Francine Riedmayer [toddler] doesn't really care what happens as long as nobody leaves her in her crib too long. She wants to explore the world!
Quinton Riedmayer was another product of the random name generator. I liked the name enough to build a whole family of names around it, but then when I actually started playing I kept thinking of that Sim as Jack, no matter how many times I reminded myself that his name is Quinton. So I built part of the backstory around that oddity.
The twins are biracial. Their father was quite handsome despite being taken straight from the randomizer; it's too bad I had to delete him. I used a different male Sim for Francine, and it worked out such that it's pretty obvious she's the twins' half-sister, which is what I intended.
The elderly brothers are both naturally fair-haired, though Elwood especially has a pretty good tan going. (I think he's blond under the gray, and Jack is a redhead. But it might be the other way around.)
Jack is a Capricorn (which means he's kind of shy and very playful) and a Romance Sim whose lifetime aspiration is to have 20 loves at once.
Elwood is an Aquarius and a Fortune Sim whose lifetime aspiration is to make $100,000. Funny, that's exactly like Darius Kules.
Beata is a Scorpio (very active, kind of low on niceness) and a Popularity Sim whose lifetime aspiration is to become a General (top of the military career track).
Edith is a Capricorn and a Fortune Sim whose lifetime aspiration is to own 5 top-level businesses. That's going to be...interesting.
Joan is a Leo (10 outgoing, at the expense of everything else) and a Family Sim whose lifetime aspiration I forget. I think she wants to graduate 6 kids from college or something.
Francine is a Virgo (shy, serious, and very tidy) and will be a Knowledge Sim once she's old enough to have a real aspiration. I rolled her aspiration with everyone else's, rather than waiting to roll it when she became a teen. Virgo is pretty much the perfect personality for Knowledge, so she should do well in life.
The Riedmayers have a lot on the south side of town, near the water (I'm not sure if it's an ocean or a lake or what) called Riedmayer Cove.
Also, Riedmayer is pronounced Reed-my-er. I'll let you figure out first names yourselves.