I'm currently 28 weeks pregnant with #5, and my baby of the bunch just turned 1. It's totally doable, but you really need to find a babysitter. I live in a small town and bring my kids to do title searches, deal with the town, talk to the assessor, an drive-bys on properties, but I would never ever take my kids, especially the baby, to meet with clients. I don't need that distraction and while most of the clients I have know I've got a handful of kids, they also know that they have my full effort and attention. When the baby was smaller and confined to a carseat I would take her to REIA meetings, she refused bottles and no one ever seemed bothered by her presence. My older kids have gone to plenty of meetings. I bribe them with use of their tablets and a soda, they will sit quietly in the corner.
I found a sweet older woman with 6 mostly-grown kids that is the perfect on-demand sitter. She doesn't work, and her her grand babies are 8 states away, so she loves on my kids as substitutes. She comes to my house, if you have such difficulty trusting people you can put up nanny cams. Ask the other moms you know/meet and I'm sure someone will have a local solution for you and know of someone available. There are going to be times when it's just super unprofessional to be toting kids around, like to a closing at an attorneys office!
I use my time while the kids are napping or at school to make phone calls, but do most things via email. I show property in the evening when my husband gets home from work or on weekends, that tends to wok best for my buyers anyway.
Real estate is super flexible and a great career choice when you've got kids, but the reality of the situation is that you will need daycare of some sort, even ifor it's just a babysitter that is on call and available a day or two a week. It sucks leaving babies in the beginning, but you'll quickly "get over it". Honestly, I'm rarely away for more than a few hours anyway, so it after the first few times it won't be as rough on either of you.