I really don't think Kody is more in love with Robyn than the others as a whole. I think he spends more time with her because she has younger kids. So she can use that as leverage, she needs more support etc and he loves younger kids.
Because they're still in that phase where they make him the centre of attention, which he loves, and still in that phase where Daddy is the greatest man that ever lived. The hero. He loses interest once they start to have their own opinions and lives and aren't always interested in doing what Daddy wants to do. Robyns 2 youngest will still be excited to do whatever Kody wants to do. We saw when he was trying to force Truely to ride a bike how pissed off he was that she was asserting her own will and didnt want to do what he wanted her to. Unless you're interested in what Kody is interested in; guns, wrestling, manly pursuits etc then he's not too bothered. Thats the only reason he found it easier to 'bond' with his boys. If they'd have been interested in cooking, online gaming or a million other things, he wouldn't have got involved.
I think he was smitten with Robyn originally but shes not the hot, younger new wife anymore. Shes now approaching middle age; ageing and widening rapidly and becoming more disagreeable and miserable year on year. She also doesn't view him as her hero rescuer anymore.
He HAS to be the centre of the universe, the best man in the world and the hero. The only people giving him that feeling anymore are his youngest kids and Grandkids. Thats why he's with Robyn more in my opinion.