I am the eldest of 2 children. My mum has always been a difficult character. Very intense, full on with love, or full on with anger, or some other emotion. No real shades of grey. I was (probably obviously) a very compliant child and have always done as I was told, as I was/am a bit afraid of her - she has what I can only describe as temper tantrums. But, well, she's my mum and I love her.
My dad died about 6 months ago after a short fight with cancer. Mum and dad were a very balanced couple, with him being the total opposite of mum, and he held her in check most of the time (or at least away from me)
Mum's emotions have, understandably, been up and down a lot since dad died and as I live closer than my younger sister, I have been mum's main source of support, though she is starting to rely on me a lot less these days.
I am married, with a young child and am pregnant. I feel, in myself, very emotionally "closed", though other people say I do not come across like that. I am balanced, though do have a short temper (esp. in pregnancy) - and due to my emotional "closedness" I am unable to properly assess how I ought to be feeling, hence asking you for your opinion.
Mum keeps in contact with my dad's mother (my paternal grandma, who is in her late 90's and going strong) - although they have always had a tricky relationship. Mum feels sorry for Grandma and so invited her down to stay with us for a few days (with my consent, as Grandma would be staying in my house). the care of grandma was to be shared between me, my mm and my sister, though I realised, and appreciated that the main care of her would fall to me.
Grandma arived a couple of days ago, and mum instantly had a row with her and said "I don't have to put up with this these days" and stormed out 
My sister came over and helped me look after grandma, she is physically able, but needs to get around in a wheelchair, and can't hear well so talks over my daughter when she talks etc - so it's a bit difficult juggling everyone's needs if I am alone. DH also helps me now as its weekend, but works in the week.
It had been agreed, before mum having her flounce, that Sunday we would potter around home with grandma, and possibly have a family roast in the evening, Monday me and mum would take grandma and dd out for the day, and tuesday mum would look after grandma as i needed to get back to work (self-employed) and she goes home that day.
Mum has since said that she is no longer helping me as she cannot bear the woman, has booked herself to go out all day on monday leaving me with grandma and my daughter to entertain all day, and has also said "it won't hurt grandma to spend Tuesday by helself until I collect her for the aeroplane"
Obviously I won't leave grandma here alone, she lives alone and likes seeing us - so I will not be working on Tuesday.
I feel so utterly let down. DH is fuming, he would have taken a day off work to help me get around with everyone if I had planned it that way, but I believed I had a bit of help. I cannot quite believe that mum would be so selfish to dump ME, never mind about grandma, she should be helping me, her daughter, as I am the one who will be upset, grandma probably couldnt care a toss who looks after her. Especially as I regularly go out of my way to make sure mm is okay, and looked after, even when I have other things I want to do.
Mum is also being short and a bit mean to my daughter, and TBH right now I don't want her around me.
I have just had a conversation with mum about monday and it ended with her telling me she is inviting herself to the roast dinner here tomorrow night. Right now I could honestly cook and carve my mother for sunday roast - how fucking dare she think she can come for the good bits, but leave me to cope with the bits she doesnt want?
I guess (if you've read this far) I want to know AIBU? And how on earth should i handle my mother? Would it be better if i just ignored her childish tantrums and ignored her - told her there is no roast tomorrow, and perhaps we eat with otu her (this is what i am most minded to do) or do i confront her and tell her exactly why she has let me down, how i feel and the fact she has upse my daughter too? This makes me feel like it the RIGHT thing to do, but i doubt she will elarn, she will cry and be a bitch to me until I apologise 
help please?!