Gosh! A lot of replies, and much food for thought. Thank you everyone.
A few thoughts/answers/updates:
I probably should have been more specific about "day-tripable". It's a 3hr round trip, so too far to meet for just a coffee. A full afternoon as minimum is usually expected, and I think that's fair given the travel time involved.
That probably also answers the question of why DH can't take DD to see MIL between feeds! But even if we were bottle feeding, would many mothers be happy letting their 2 month old go off for the day with Dad without them? Maybe I'm more PFB about her than I thought 
The open house suggestion...perhaps it is sad that I don't do that. But it's the way I am. Actually, if I lived in close proximity to lots of friends and family I might enjoy having more of an open house, because visits could be quick and low-key. But who knows? Maybe I'd still guard my privacy jealously! I do believe that introverts come under a lot of pressure in this society to meet extroverts' expectations.
I have really taken on board people's suggestions to make the visits specific to something - so, would MIL like to join us on a trip to the zoo? Could MIL please help me out as I'm dying to decorate the baby's room and need someone to cuddle her while I do it...etc. etc. I know that MIL would truly like to be helpful, and that it upsets her that I don't really need much help, so I could try to create more need for that.
Someone asked about how often DH saw his paternal grandparents. Unfortunately he has never known them, so the only comparison DH/MIL have for this situation is the relationship they had with his maternal GPs.
DH and I spoke about this again this morning, and he's agreed that fortnightly is a reasonable compromise, and we're going to try alternating weekdays/weekends as several people suggested. He's not overly happy, but I think he's beginning to recognise that forcing more is not a good idea.
I honestly do want DD to have a good relationship with MIL. I would hate to be a barrier to that. It's just about finding a way to let them spend time with each other in a way that I don't find horribly intrusive.
As for the issue of childcare once I go back to work, that's going to be hard to agree on. I would like to use a childminder. DH would ideally prefer me to stay at home, but knows I want to return to work so has suggested his mother two days a week so that DD doesn't have to be with "strangers" all week. I'm not keen, not least because MIL is quite absent minded, but also because I don't want to clash over child rearing methods (which we would). I'd prefer MIL to be special to DD as my GPs were to me. Putting her in the position of having to deal with DD warts and all, having to wean, cope with tiredness, illness, discipline - that IMO would take the fun out of their relationship.