Random emails from companies are rarely legitimate so you are wise to have investigated. It's no surprise that they seem to be scams.
There are some legitimate jobs like medical transcription but those require a certain skill set and sometimes certification. You also need to seek out the clients. There are also deadlines and it's tough with a newborn who may not cooperate with your schedule!
Direct sales is a very good possibility - it's the fastest growing segment of the workforce, as people take more control of their time and finances. People are so tired of giving all their time to corporate America - like your husband, they are working 2 jobs, and like you, they want to spend time with their kids. Companies used to be loyal to their employees, keeping them for 25 and 30 years, but now they are downsizing and cutting benefits.
If you want an in-home business, be sure that the company is a member of the Direct Selling Association. That's a watchdog group for network marketing companies, and only the most reputable companies who adhere to DSA standards are invited to join. A company cannot buy its way in just by paying dues - their books have to be scrutinized for a year, and the company is evaluated for reliability and distributor satisfaction. There are only about 200 companies in the DSA, out of the 5000+ companies that operate in the U.S.
Then, make sure that the products you are selling are things that people need every month. Giftware, toys, household goods, jewelry - people buy once and then not again for a while, if ever. My SIL sold for a very good toy company (good quality) but she had to keep finding new customers every month, and she was always out doing home parties. Plus, her market was only people with children. Another friend sells jewelry - again, great quality - but her market is only women who wear silver. These are things people cut back on during a tough economy.
The next trillion dollar industry is slated to be the wellness industry. (The last big one was computers - imagine if you'd gotten in on that in the early days!) Our food is less nutritious (despite being more abundant), and our kids have record rates of food allergies and behavioral problems and diabetes. The baby boomers are aging and don't want to be! So people are taking care of their health and doing a lot for prevention since the medical/health care system is so ridiculously expensive. Nutritional supplementation is part of most people's lives - at least 80% of people take something on a daily basis. Unfortunately, most of those are individual ingredients (Vitamin this, Mineral that) or something based just on vegetable or fruit juices, which are not effective. But the American Medical Association recommended about 10 years ago that everyone take a comprehensive supplement, and there are a few companies who are both part of the Direct Selling Association and also on the Council for Responsible Nutrition, which is trying to increase the standards for supplement companies. Among those few, you want the one with the best compensation plan so that you can get the most money for your time. That's what I do. Everyone is a potential customer - man, woman, child. And I can do it on line and all over the country (the world, actually) and am not restricted to home parties.
Be careful of a company that only lets you sponsor 2 people beneath you who have to build evenly or you lose your profits (a binary system), or that has monthly minimums or purchases required. Make sure you don't have a big investment or membership fee, and that you aren't required to carry a large inventory (jewelry and toys, for example, require that you have a lot of items on hand to show at home parties). You want a company that lets you sponsor deep as well as wide, and that has multiple avenues of income (retail, wholesale, overrides, bonuses and so on). Also be sure that if you sponsor someone who rises to your level that they don't "break away" such that you no longer make money from their sales. My company has 5 avenues of income and has the highest rated compensation plan in the DSA. And businesses are guaranteed for a year so the risk is minimal. Make sure that the company trades on the stock exchange - that means they are not a scam and that the Attorneys General of all 50 states have not issued a complaint or an investigation.
So those are some guidelines to help you figure this out! Let me know if you want more info.
Good luck!