Hi Wes. I just want to comment on a couple things. You said that you haven't got anything to lose by asking her to lunch and it didn't go great, not bad, but certainly not what I'd consider to be working. Then, you called to ask her if 'she gets bored or lonely' she is welcome to join you and the kids for an outing.
Sorry for the slap that's coming your way, but are you crazy? If my H gave me an invite based on me being bored or lonely, I wouldn't even think about going and he's the walk away! Accepting that invite would be admitting boredom or lonliness. You've got to think about how you say things before you say them.
Perhaps you feel that you're so close to D, you don't need to monitor, and weigh your words, and allow your actions to speak, but you do!
So, you can sit back and think that you've already lost and continue on as you are OR you can slow down for a bit and think about how you can make this better. What can you do to make yourself more of a friend to her? I'm not opposed to you inviting her to family outings with your kids or both kids or whatever; just make it a friendly one. You and the kids are doing such and such, and you'd be happy if she could join you guys or whatever.
Here's the thing though, you had a so-so lunch, and a not so good invitation to spend time with you, so please lay low for a few days.