I did something similar a while ago. There are several things you can do:
There's something vaguely similar called Weapons of Legacy. Is a 3.5 book that, despite being a bit weird rule-wise (actually the rules are pretty bad, as per @DuckTapeAl and @KRyan mentioned in the comments. Use it for ideas and flavor only), can give you good ideas of how to implement a legacy in the form of Magical Weapons from their parents.
Secondly, you can make the player's kids inherit some of their scores from their parents. Let's suppose that Mila the Wizard and Bronco the Barbarian marry each other and have a nice, beautifull little girl.
For each of their daughter values, toss a coin. Heads, she get that score from her father. Tails, from her mother. This way, you could have kids that look alike their parents someway, at least ability-wise. This could even create interesting characters: if Mila and Bronco had five kids, each one of them could be vastly different from one another, depending wich scores they get from their parents. You could have a "super-genius, super-strong kid", with a wimpy, always sick and... slow sibling.
If you go this way, more powerfull parents would make more powerfull offspring, which, in a way, kinda makes sense.
Then, you always have the cash from their parents. Those kids could start the game with better gear, on even on a higher level - if there is enough money, you could "pay for an extra starting level" to represent all the extra training the kid got while growing up.
You can also play this "legacy" as influence. People know the kid's parents, and thus would gladly repay all those wonderfull things that her parent's did when travelling around the village.
Keep in mind, however, that the game is played better if everybody is in a similar power-level. A single level of difference in 3.5 is huge, and thus make sure that every single player receives equally good benefits.
How to spend money with my family?
There's a few ways you could handle that. You could go the "Hardcore way", and track every penny that you spend with your family according your desired lifestyle. You could go a really abstracted, and spend a fixed amount of money per month and that's it.
What I do is something like this:
I set for every character an "Average Family Upkeep Cost", that the character must spend every month according to the desired lifestyle. This value includes basic stuff like food, taxes, rent (if applicable), clothing and other basic needs.
I also offer several "Add-ons" for a family, that can be paid on a separated budget. Those add-ons include teachers, sword-fight trainers, and several other professionals that teach or train your kids.
Each "teacher" have an associated cost per month. For each 6 months a kid stays on training with a given teacher, it gets a half skill-point on that teacher associated skill. For teacher's that give a more class-oriented tutelage, every few years under training equals a class level.
A kid can only have as many tutors as it's Intelligence Modificer (minimun 1), so smarter kids can learn more stuff on the same time than other not-so-smart kids.
Of course, you should respect different "dificulty levels" for each class. Training as a Wizard is way more demanding than training as a, let's say, Fighter, so you must adjust the costs of the tutor and the time of training accordingly.
To control all this stuff, create a small "family sheet". About a half-page should do it.
On that sheet, write up every family expense, includding teachers, and the total montly upkeep.
If, by the end of the month, the character can pay everything, that's fine. Write up the coin that was left off, and move on. If the character can't pay everything, he must then negotiate/borrow the rest of the money, or give up some of the services that he acquired for his family.
Don't overcomplicate stuff - unless you really want to keep every single single penny spent, I suggest using whole numberns and more or less adjusting costs to simplify the book keeping.