Hi,
I've never had a baby and only been involved in taking older kids on holiday so can't offer advice from direct experience re the baby's needs but can offer advice with regards to multi-generation family holidays. And the best advice I can offer is to make sure that everybody knows what they want from the holiday and ensure that these are compatible. I have been and still do go holiday with my parents, my brother and his family as well as with wider extended family groups (up to 50+ people for one memorable Hogmanay houseparty!) and they only work if everybody lays their cards on the table before we go and makes it clear exactly what they want from the holiday and we establish the mutual expectations and ground rules before we even depart. And those that have really worked best are those where everybody knows that nobody expects us all to live in each others' pockets for the duration (so literal and emotional space is really important) and that everybody can take some 'me' time at some point, where everybody feels that their needs are being met in part and nobody is left feeling martyred (or takes on the martyr's role) because they've spent the whole holiday fitting in with other people's plans and never got to do any of the things that they want to do.
It could be great for you to have a ready made babysitter on tap but do check with your Mum first that she is prepared to do this. A friend of mine has only ever been on holiday once with her son and his family because she soon realised that she'd been invited in the expectation that she would babysit most evenings so that son and daughter-in-law could continue to have the same sort of holiday that they'd always had pre-babies without this ever being discussed in those terms with her. She found it really difficult once they were there to put her foot down and say that she wanted more from the holiday than spending most evenings on her own in the villa with only the sleeping grandkids for company. Her daughter-in-law resented this and my friend resented the fact that she was supposed to feel grateful that they'd asked her to go on holiday with them. Instead she's actually come away with our lot instead and we've had a good mix of me and her getting some grown-up time to ourselves away from the kids and equally us being more than happy in return to take the kids swimming, leaving my parents and/or my brother and his partner to have a bit of down-time. And now that the kids are older and so are we, we all go out together for dinner and are all ready for bed at around the same time :-) I can see the time fast approaching when my nieces will see the 'wrinklies' safely off to bed before they hit the town on their own!
Evenings tend to be a bigger bone of contention than the daytime so before you go, sit down with your Mum and talk about and agree what will happen. You've lots of suggestions here as to how you can manage bed-times, the pros and cons of putting your baby in her buggy and taking her out with you for dinner etc and whether you will or won't take it in turns to babysit etc, because whilst your Mum probably wouldn't want to go out for dinner on her own or just with your husband while you babysit, she might really appreciate the offer from him to babysit on a couple of evenings so that she and you can go out together and have a real, baby-free mother-and-daughter chinwag over a meal and a few drinks.
In a sentence, before you go, sit down and talk through what you all expect of each other and what you each want to do, rather than just assume that you will all want the same things from this holiday. Get that right and the practicalities of taking a young baby away will be a doddle :-)
SM