There's one strategy that I've seen to be effective when MIL insists on calling herself mummy/mama etc, although you'll need to get your DH on side and actively involved...
Your MIL is a mum - to your DH. So every time that she refers to herself as mum deliberately misinterpret what she says and make it refer to your DH. Does that make sense?
So, for example, say she said something along the lines of 'mummy got you (ie DD) this cute toy', then you say 'I think DH is a bit old for IgglePiggle'. Or if she gets her a little outfit and says 'Look at this cute outfit that mummy got you', DH can say something like 'Thanks Mum but I think it's a bit small for me and pink has never been my colour...'.
You know she is not going to like it when you do this but on the other hand, you don't like it when she calls herself mummy. Psyche yourself up in advance, think of it as a game, if she has some stock phrases that she uses, make up some good responses in advance and see how long it takes for the message to sink in.
And as myermay says, you need to have the conversation with her to explicitly ask her what 'grandma' name she wants to be called.
Have you got a bank account set up for your daughter that you could give her details of so if she feels the need to spend lots of money she could pay into it? there was something on moneysavingexpert.com about a Halifax account that was a good one for kids that you could put a fixed sum into up to a maximum of £100/month. (details are on their savings for kids special page). From what I can gather, you can have several of these accounts but only one person can save into it for the kid - so you could have one that is set up explicitly for her to pay into, and for the first year at least, it gets 10% interest which is pretty good. If your MIL wants to splash some cash, could you encourage her to put it into something like this for your dd ('for her uni/car/house deposit/etc when she will really appreciate it and thank you for it MIL...'). She can even play competitive granny-ing with it because she will be able to see what she is putting in IYSWIM - or at least you could spin it to her in that sort of way.
Any chance you can get receipts to take any of the stuff back/or encourage her to do so? Or get her to leave some stuff at her house to be played with (ie not used lots) because you don't have storage for stuff? Or ask her to help out looking after DD while you go and sell everything at the NCT/whoever nearly new sale...
It's miserable having a MIL like this - but if you know she is going to do it, take a deep breath and turn it into a game in your head and then you can turn it around more easily. All sorts of ways of doing it (have posted on it before but can't remember where, sorry) - have a MIL bingo card with all her nasty sayings and habits on, to cross off as they occur. Promise yourself a glass of wine/big bar of choc/ long soaky bath/new handbag/whatever when you fill up the card or get a row. Or bet with your DH to see who will get their card filled first. etc etc - you never know, you might actually be wanting her to call your DD 'mummy' just one more time so you can finish your card and have a legitimate reason to go get that pair of shoes you have been eyeing up or that bar of choc that has been sitting calling to you from the shelf...
good luck!