I’m not sure I understand why those things have to be mutually exclusive. Who says you have to give up an income because you stay home to raise your children? There are plenty of things you can do to bring money in, even if you don’t hold down a full-time job outside the home.
Especially given that you’re using the internet and posting this message on an internet website, I can’t believe no one’s yet mentioned all the ways you can make money on-line. My mother used to create crafts and gift items and sell them through consignment shops and boutiques. You could do that and sell stuff on-line. Start out selling things on one of the on-line auction sites, then eventually you could have your own site where people can just order directly from you.
Learn how to do HTML and start your own website design business. The hours are as flexible as you want them to be. You could work on graphics, page design, search engine submission, etc. while your kids are napping or asleep for the night - the internet’s open 24 hours a day. 
If you don’t want to create websites for other people, create one for yourself and get advertisers to place banner ads on your site. A friend of mine created a soap opera message board that gets hundreds of thousands of hits every week and he makes between $40,000 and $50,000 a year just from the advertisers!
There are other ways you can use your computer to make money as well. Start a resume writing business or do medical transcribing.
If you’re really concerned about socializing your child, do daycare for other children in your home. Then you’d be making money and having your child interact with other children in a daycare type environment, but you’d be in charge.
And if you want to expose them to other children, but not have to be the caregiver to other people’s kids, there are a ton of things you can do outside your home that will serve that purpose as well. Join the YMCA (or YWCA) and bring your child to swimming lessons or any of the other myriad activities that they have designed for kids to participate in. Find out who the other parents are in your neighborhood, or find other members of your church/synagogue who have children and start a “play group.” Your kids will have other kids to be with and you’ll be with other adults at the same time.
The bottom line is, you don’t have to forego an income or be hermits, locked inside your house in isolation, just because you choose to raise your children full time instead of working outside your home.
Good luck with whatever you decide to do.
“How wonderful it is that nobody need wait a single moment before starting to improve the world.” - Anne Frank