Welcome to the forum! Yes, any undertaking is very exciting and a little scary. To find companies in your area I would suggest you sign up with the free version of Jobslinger.com and see who is advertising shops available in the areas you mention. While the shops have likely been taken already, those companies will continue at least through the calendar year to have those shops come up time and time again. These are the companies you want to be signed up with.
Congratulations on having completed your first shops! As you will see, you probably got a nice meal out of the restaurant but not much fee for it or for the phone shops. Only you can figure out whether this is an economical endeavor for you.
Many shops do not allow bringing children along and for detailed shops it is generally not advisable to bring along young children who might be a distraction to you. So age of the children may be an important factor for you.
On the positive side, if you can be home with your children you can save a lot in child care costs, working wardrobe, work day expenditures such as coffee, lunch, afternoon snack etc. Often mystery shops have useful reimbursements which can bolster the household budget by providing some of the groceries, oil changes and entertainment tax free. And you will find that a good portion of the fees you earn (that are taxable) are offset by the IRS mileage allowance for using your car so that bottom line you have made little if any profit. Not having a tax profit is not the same as not being profitable. You currently are needing to cover the expenses of your car anyway (licensing, insurance, gas, maintenance, repairs, depreciation) but get no tax advantage for using your car to commute to work. You do get a tax advantage for using your car for your self-employment.