]if Lady had wanted Anne to be removed from Kellynch once in a while, why hadn't she invited Anne to go with *her* on her trips instead?

I can't imagine Lady Russell--who, to my mind, truly and dearly loves Anne--neglecting Anne, even if unintentionally. Can it just mean then that Anne, melancholy as she seems to be, just refuses Lady Russell's previous offers and declines to have a change in society?

I suppose it's possible that Anne has refused past offers by LadyR but under the circumstances, it doesn't seem likely to me.
If LadyR had made previous offers and been refused, why would she continue to lobby for Anne to go with Sir Walter and Elizabeth? Why would she think Anne more likely to accept an invitation to go with those two meanies if not herself? I think Anne actually would have accompanied LadyR to London or perhaps even Bath if she had requested as her to come along to keep her company. At this time, this is just my humble opinion but I think further support is yet to come so more later. :-)