First, DO NOT p*ss away even one dime on any sort of real estate investing class, home study course, boot camp or mentoring program. If you and your wife want to start a business, start one that leverages your current knowledge and skills. Real estate is a business like many others, and has its own set of knowledge and skills. You can learn a lot from reading here, reading books, and from all the various gurus who are out there selling education. But it takes time and effort to learn a new business from scratch.
Rental real estate does not produce much income. Certainly, anyone who tells you "this cash flows. Rent is $2000 and PITI is $1500, so you'll have $500 a month in cash flow" is lying. You will have vacancies, maintenance, advertising, legal fees, liability insurance, and numerous other expenses beyond taxes and insurance. Rentals are great for building long term wealth. They are bad for short term income.
Other forms of real estate businesses, like wholesaling, fix and flips, developing, and the like are jobs. They are risky jobs because you only get paid when you make a deal. Some folks are very successful at these. But easier to get started if you don't have to worry about putting food on the table.
You need to fix your income problem, first. You say that you were approved for a loan on a second property. Current lending guidelines won't allow any of the potential rental income on your existing property to be considered when approving this second loan. That's because a common scam is to buy a new, cheaper house, claiming the old one is going to become a rental, then let the old one go into foreclosure. Banks have gotten wise, so, the lender would have looked at your combined income and the new and existing payments, and only OK'ed it if you could handle both with no income. Now, if the two of you could handle both loans, it seems like you should be pretty close to being able to handle the existing house on just one of your incomes.
Can you wife find another job in a similar field, even if it doesn't pay as much? Can you get another job?
Is something happening with your current loan, like a big reset in an ARM rate? Even so, seems like the new lender would have been aware of that.
If you have $40K available, that sounds like a pretty good emergency fund. If you're close to being break even, can you tap into that money to stay afloat while your wife looks for a new job?
Now, some folks do take an opportunity like this to make a major leap. And leaping into real estate works for some folks. But, its tough and its a lot of work, and the paydays are sporadic and depend on your skills and abilities. There are also a lot of people out there ready and willing to separate you from your money. Folks who can spin a very good story and make you think you're going to rich while the get you to max out your credit cards. Don't become a victim.