Without knowing your skill set and interests, it's difficult to know how to advise you. My husband and I both work from home (in different areas) so we have plenty of experience here.
It seems to me that you have 3 main options.
One is to find a job within your current company that does not involve traveling and which could be done part of the time at home. But if that were a choice for you, I think you'd have seen it already and wouldn't be posting here. So either your company doesn't have (and won't consider) an option like that, or your skills (and their industry) is completely unsuited to at-home work. No employers will pay you to play with your kid, as other have said, and no work on deadline can be completed if the worker is dealing with laundry, playtime and housework.
The second is direct sales. The comments frequently made on this site about direct sales and multi-level marketing show a lack of understanding of the industry. MLM is completely legitimate IF you have a legitimate company. Like corporate work - there are good corporations and terrible, dishonest ones (just read up on WalMart, for example, or any company where the top owners/CEOs are making all the money while the workers labor for minimum wage and few benefits). MLM is endorsed by so many economic experts, from Suze Orman to Robert Kiyosaki. Companies in the Direct Selling Association have been evaluated for their ethics and employee satisfaction, so that's 200 companies for sure (out of 5000+) who are good choices. BUT it's absolutely work! You must be self-directed, self-disciplined, have a good product, and not be interested in hawking products to your friends all the time. With a good company and a good compensation plan and excellent/free training and no big cash buy-in, you can make money based on your own efforts. You don't have certain benefits, but you have a lot of advantages of an in-home business including significant tax deductions. But you have to get up, get dressed, go to your in-home office, get on the phone, and do the work. You have to put in the time to build an organization that pays you every month. There are ways to evaluate a company and its products/comp plan but don't think that you just sit at your kitchen table and the phone just rings and rings. You have to be entrepreneurial in nature to make it work. You have to build a network - the people who don't do this are the annoying ones who are always nagging their friends and relatives to purchase something. You need a product or service that everyone needs every month, not just giftware for holiday giving or something that can only be marketed to a small niche market.
A third option is to have a skill that's in demand, and to be able to work/schedule well. My husband is a copywriter and has worked from home for 20 years. He's either working on an assignment or calling ad agencies who use freelancers or calling companies directly. He gets referrals because he's well known and has won many awards, but that means he's put in the time already. It's a business of client-nurturing as well as writing - creating a network of sources and juggling the assignments as they come in. A friend of ours is a freelance editor - it requires writing skills but very different from the ones my husband uses. She's also working on referrals and contacting newspaper/magazine editors, creating a network, and building on that. Even people who do artisanal work (making anything from baby items to furniture or pottery) have to network it, get into shows, develop a referral list, and so on. That's not sitting around the house. All of this work involves deadlines with no allowances for a sick child or a beautiful day to take him to the beach. However, your years in the corporate world may have given you a good base of contacts as well as skills. If you are well-regarded and self-disciplined, this could work for you.
So you see, you either stay with the company you have, or you do something that builds a network.
I suggest you analyze your skills and interests, and that you take a few days off and actually keep very careful track of how much time you have to do something other than enjoy your child. Sit and read a book - something uninterrupted and requiring focus. See how far you get. Also count the interruptions - how many times you got up to empty the dishwasher, throw in a load of wash, pick up toys, deal with a booboo. If the child naps, those are the hours you have. If he sleeps at night, those are the hours your have (make sure you husband doesn't expect to spend time with you). If your husband or your mother or a babysitter can take him for part of the time, you can work those hours. But you will not be with your child during those hours anymore than if you were at a corporate job. You won't have commuting cots and wardrobe costs, and you won't be traveling (so at least you will be home every night), but you will find you don't have 40 hours without plenty of help. Maybe you have 10? 20? So calculate the hourly wage you would be paid and subtract babysitting costs.
Serious self-analysis and reflection, as well as an objective calculating of your true available hours as well as when during the day those occur, will give you an idea of what you can reasonably accomplish. No matter what you choose, it will involve time away from your child.
Good luck. Hope this helps.