That's interesting strugs and a few things you have filled in about the background to this suggest some various dynamics going on, which makes me feel it's not really your DIL who is blameworthy and responsible for your feeling left out.
Firstly you seem to have been very diffident in expressing your feelings to your son "a bit left out" when it seems youre actually really very upset. But your son did respond to this, albeit clumsily, and your DIL reciprocated, even though I think the majority of DILS would not want to be tied into seeing their MIL every week. Where there is a higher frequency of contact it's very often because the MIL is doing childcare for them, not because the DIL is just calling for a chat. It seems as though your son wasnt even involved in these contacts so the responsibility is falling to DIL. Could he facilitate contact by calling in at the weekend with the GD taking the burden off her?
The other thing is that MatGM seems like a very forceful character, probably worried that because they are so far away and you near that she risks being upstaged by you! You do after all see GD in RL with greater frequency than MatGM even though your time spent with her is less!
I wonder if in fact MatGM wasnt so obsessed and clingy, would you be happier? It may be that MatGM is even more involved than DIL really wants her to be but DIL loves her parents and doesn't want to upset her. Staying for so long and every month does sound excessive. It may reduce though when MatGM has other GCs, and DILs DCs get a bit older. Will they even have room to put them up for so long when they have two?
So ways of dealing. You could accept that seeing your GD once a fortnight, while not as often as you like , is still far more frequent than most GPs who live further away see their GCs. Your GD is happy coming to your house, and she doesnt have big gaps in which to become shy and more distant, congratulate yourself on your good relationship and enjoy it, viewing desperately clingy matgran as that and don't try to be like her. GD is not necessarily going to prefer her for it, in fact as she gets older she may even find the over frequent visits annoying as may your son, and he might put a stop to some of them.
You could ask your son to bring GD over, or invite the whole family over at the weekend for lunch occasionally. Your son needs to take responsibility for facilitating your contact by involving himself I think, not bulldozing his wife into scheduling you in when she is alone at home.
Lastly since so many local PatGrans who do have a lot of contact do so through childcare, would this be an option for you? Making yourself a useful unpaid carer is more likely to raise your value to DIL. You said she works part time, well would you be up for caring for the GD one of those days, saving them nursery fees? Do you offer evening babysitting so they can have a night out? Its not much fun in that GD is going to be in bed but youd probably get to go round a little early and do the bedtime story. Its also a way to see the whole family and get to know DIL better.
It would be interesting to see if any comments come from PatGrans who have been able to improve contact and relationship with DILs from a weak base. So often theyve either been lucky and hit it off and seem a bit smug about it or theyre feeling very cut out and annoyed with DIL.
Being moved along by someone who "wants your place".
sticky labels on apples - remove before washing!
How much do you spend on yourself?