Thanks all, I really appreciate your comments... I'll be honest and say that I was quite surprised at how many of you seemed to think this would be a big ask and also didn't think it would be a good arrangement!
I'll try to cover off some of your questions/points.
I don't expect help with my childcare arrangements, and none of the grandparents are under any obligation at all and I intend to make this perfectly clear to them. I'd hate for them to feel pressured, but I also think that we all have a good enough relationship for them to say no if they don't fancy it. They are all very doting and I guess I'd imagined that actually, come DD being 1ish, it would be "normal" for them to take DD out for the day or for her to spend more time with them without me just that this formalises the dates a bit in advance.
The £20 would be more to cover expenses for the day, contribution to some petrol, a coffee, the fair, the cinema, lunch, whatever really..
I totally get what you're saying re "days out" vs "childcare days" and have rethought my thinking (IYSWIM) in that actually any time spent with each other should definitely be seen as a treat, by DD and by the grandparents. Thank you for that.
I don't expect the GPs to replicate me and I know they've all bought up their own children so are capable of looking after DD, but I would like them to listen to say, ideal or rough nap times, food preferences, and general respect for the fact that I am DD's mother and have worked effing hard to get to where we are now.... I don't want to write a manual, but I would like to be able to say "if she doesn't nap for more than half an hour, can you try and get her down for 2 short naps instead" or "strawberries give her a rash" or similar? My mum listened to nothing I asked/said when she had DD before and had a nightmare during feeds and at bedtime. I'm sure at 12mo DD will be a different baby to when she was 4mo and feed/nap/bed times will be more fluid than back then, but my mum didn't even listen when I reminded her about the blue tube thing that goes in the Dr Brown's bottles!! Mum also tries to prove me wrong with things or suggest that she knows DD as well or better than me. She has a habit of saying things like "ooh mummy says we can't" or "naughty mummy" or rolling her eyes when I ask her to put a bib on DD when she's eating a satsuma as the last time she didn't, it stained and ruined a brand new (and expensive) top!!! DD doesn't benefit from any of those things and it just riles me! Hmm, I suspect that's a new thread in itself!
My stepmum, in her own words, feels like the "3rd granny" after the two biological grandmas and I'm really trying to ensure that this isn't the case and that her and DD's relationship is as sturdy as the others. So I would feel that just asking my dad to help would make my stepmum feel even more ungrandparenty. I can't change the fact that she works full time, but I don't want her to feel left out of the child-care considerations, so I figure by saying to her "I'd really love it if you and dad could have DD for every third Wednesday, but I understand this means you taking time off work, so please have a think and let me know your thoughts and I'll totally understand if you don't want to or can't do it" (or words to that effect) I am showing that I am asking her primarily, not just my dad because I trust her with DD and want her to be involved.
With regard to MIL - she also has every other weekend (Sat/Sun) off as well, so not just Mon and Tues. She has been very keen to see more of DD anyway, so I'd thought that having a dedicated date in the diary might be something she'd like. Also, MIL waits to be asked when it comes to seeing DD or popping over (whereas my mum just turns up) so it's very much her style to hover in the background.
In terms of DD and what's best for her... Well, I think that her having one-on-one time with her grandparents is important and will benefit her (and them) so this is primarily why I'd like their involvement. We can afford 3 days at nursery, it's no more or less convenient dropping her at theirs or at nursery, so I am by no means relying on the GPs for childcare. I thought it would be a nice way for DD and the GPs to hang out without me if they are happy to spend their free time in this way. In a way, I don't really see the difference between this and them or me asking to take DD out or have her over on an ad hoc basis? DD shouldn't feel too unsettled (though I appreciate going to nursery and me not being around all day every day is going to be quite a big change) as she spends a fair amount of time at GPs houses already....
If I take my mum up on the offer of having DD every week, I think my stepmum and MIL will definitely feel lower down the "grandmother pecking order" but would never say anything to me as it's not MIL's nature and my stepmum isn't sure of her place/role anyway and I imagine would feel like they'd be stepping on mum's toes.... Plus, I'll feel concious that mum would see DD much more than MIL and stepmum, so would probably spend my 2 days off each week feeling like I should be seeing them (I think I have this weird guilt thing from when my parents split up that I have to treat them all equally.... again, probably a whole new thread!).
Anyhoo............. I guess I am trying to justify my thinking to show that I wasn't being presumptious with the whole thing. I actually thought it would kill a few birds with one stone - they get to spend regular/diarised quality time with DD and it helps us out with childcare.
I plan to ask them this week once I've confirmed with that there are spaces in the nursery so will let you know how it goes.