Hello and welcome. You're off to a good start with the three companies. Use JobSlinger to see which companies do have shops in your area and sign with them first. If you decide that mystery shopping works for you and want to continue, gradually sign up with as many mystery shopping providers as you can find. They will not all have shops in your area, but you don't know that in advance. Also, MSPs lose and gain clients all the time. If an MSP doesn't have any clients in your area today, they might in time, and you'll already be signed with them.
A full time job, a newborn and getting your foot in the door of mystery shopping. Wow. I gather that MSing is to help stretch the budget or to help you afford extras. Whether time spent for the money earned is worth it, varies with most of us. I enjoy the freedom, relatively speaking, of MSing without the commitment to a "real job".