I can relate about the texting. When M (much younger) and I first started really spending time together, the texting seemed to be a complete interruption of our special time. I even found out that she'd been taking selfies to send to her suitors and texting one of the more serious ones some emotional stuff. While we were cuddled up on the couch together! It seemed like a betrayal...at first. It was a huge bone of contention for us for at least 3 of the 8 months we've been dating.
I had to realize a few things: (one or more, but not all may apply to you)
1. I can't monopolize her time ALL the time. Even expecting to control 51% of her time is coercive and controlling. Your situation is different as y'all are married with children, but still when entering into a poly relationship, part of the growing pains are going to be about what used to be your time becoming someone else's time. You're very perceptive to realize that they are in the NRE/honeymoon period and that will take some adjusting to, certainly.
2. Think of who he's texting like a a friend, not a rival. Easier said than done when you know exactly who it is of course. Realize that the person you love should be able to talk and text and interact with their romantic interest as much as any other friend or even a bit more. Even as much as you, if their relationship is going that way and you're working at being fully poly. If it was his best male friend, (assuming he's not a romantic interest) would you be cool with it?
Obviously, if your needs aren't being met, you need to voice that. And if you feel the time and place are inappropriate, have a discussion that sets out your feelings about what's right and wrong, from your perspective. His may be different. You'll have to decide if you can accept what he's willing to agree to on the matter or if you can't. Same for him. Hopefully you can come to a mutually agreed upon understanding about what works for you and what doesn't.
3. Be more independent. When I realized that I couldn't and shouldn't change M's behavior, and we'd had a talk about appropriateness, I also realized that if I was waiting around on her to be my entertainment or if I was preoccupied with what she was doing more than doing my own thing, I needed to do something that was moving me forward.
I was married for 14 years and I know that when you've been joined at the hip with someone for a long period of time, especially where the focus was on being each other's biggest cheerleader, friend, confidant, etc., it's going to be strange to suddenly have a LOT more alone time (though you have kids, but you know what I mean) to suddenly do your own thing. I had to reevaluate what even was my own thing.
You'll work this all out in time. Use the time productively.
Me - male, 42, poly, straight, in a serious relationship with Audrey, also casually dating.
Audrey - female, 20, poly, pansexual, also casually dating.