It seems that you're envious of them getting extended one-on-one time, when all your time is shared with household/family responsibilities.
You and your wife need to go OUT on dates, away from responsibilities and chores. The boyfriend can babysit, which kills two birds with one stone: you and the wife get some quality one-on-one time, and the boyfriend experiences "being at home with the kids while your partner is out on a date."
I've never been on an 8-hour "date" ... when my time with someone starts getting into that many hours, I no longer think of us as merely "dating."
Some people also recommend making friends with the other partner. That works for some, not for others. But perhaps if you and he go out for beers and talk shop, you'll be able to see him as a real person instead of just "the other man" and maybe it won't be so difficult when they're out together.
Ariakas is right that you can't have a proper conversation via text message. When she's texting him while being with you, no one's getting quality time: not you, not the kids, not her, and not the boyfriend. They can get a lot more intimacy out of one 20-minute phone call than 50 texts scattered throughout the day. Then she can hang up the phone and just be with you and the kids. I'm even in "that" generation, and I still don't find texts useful for anything more than quick status updates and exchanging basic information ("What was the number of the insurance agent I'm supposed to call?" or "Sorry, I'm running a bit late, I'll be there in 15 minutes").
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker