'She is itching to come round, but needs an invite.' She has had several, but barely visited.
This is a problem for me. If MIL wants to be invited, then why didn't she come even when she was invited several times? Is there a bigger issue going on here?
Or were those "several" invitations of the "come anytime" variety? Then it all gets back to the same issue - MIL doesn't think that kind of invite is/ fears that kind of invite isn't really an invite. I gotta admit, I'm the same way.
But I see that DD and SIL brought baby over to MIL and that she, in return, went over to visit them. Maybe she just needed that little nudge to feel comfortable.
I'm joining Smileless in saying kudos to you for handling the issue as delicately as you did. I get the DD's schedule isn't set enough now for her to plan any specific visit times. But then, maybe she should hold off until she can/let MIL know she'll make a specific invitation when she's more sure of her schedule (I realize that can take a while.) Or she should, perhaps, just make a specific date, anyhow. Perhaps the time won't turn out to be good but would it be any different if MIL just popped over and it wasn't a good time?
Just thinking out loud though. Probably you're better off not saying anymore. You gave DD some ideas, now she has to figure it out for herself. It's sweet of you to care about MIL, but she's not your responsibility.
Please just enjoy your new DGS/growing family! Congratulations!