OP i can understand both POV on this. As others have pointed out you worded things quite badly and there are some statements which do sound very selfish. But there also isn't much to go on in the OP so people are joining the dots themselves.
It isn't nice your parents and sister have been discussing this and you probably feel quite wounded by that.
I think in this type of scenario constant communication is the key. Constantly asking how they are coping? if they are tired? If it's too much? Giving little gifts and lots of appreciation. Letting them know they can change their minds at any point etc. Also understanding their 'parenting' styles are different. So what they consider embarrassing public behaviour, you do not and therefore do you want your dc brought up with those mixed messages.
In my case, my parents offered to take my dc FT for free, to mean i could go back to work if i got pregnant - they were so very desperate for GC. This didn't affect my decision to have them, but it was said often to me and DH and DH very much 'banked' it. I, on the other hand, warned DH this may fall thru, people make promises they later regret etc. DH is very much 'if you say it it is so' sort of person.
Of course now DS1 is 2 and ds2 is 4mo and over the last 2 yrs the comments have started gradually, 'well, we couldn't do full time' 'only 3 days a week' 'not mondays or fridays' 'only 2 days a week' 'only once the dc are at school' 'we'll help every now and then' 'we don't want to be tied to anything'
When you ask them outright if they will still look after the dc if i go back to work they say 'oh yes' - but they don't mean it. They just like saying it. They like telling people because it makes them feel good. It's obvious to me. Not so much to DH and he has often asked me about going back to work. I have to explain that despite what they say, they just don't mean it.
The other thing is ds1 is very 'spirited' difficult and we have 2. They only had me, and by all accounts i was a malleable blob! They also never really looked after me much in the first place - i was with cms from a baby and away on Saturdays to let 'mum do the housework and shopping without me under her feet'. So they actually had very little real idea of what looking after small dc FT would be like. Now they see they have, totally justifiably, changed their minds 
.
Also, now i see them with the dc, i have realised i don't actually want them doing the childcare. They are very much spoiling grandparents, they give constant sweets and sit in front of the tv. They disagree with my parenting style and completely ignore my opinions. They will do what they want and i have to lump it. So i am relieved in a way as i wouldn't want that for my dc.
I am disappointed that they made promises they can't keep, but i do completely understand it. I am disappointed i can't go back to work now, but it is the reality of our situation.
If i were you OP i would try to speak to them again. Draw a line under it and find alternative arrangements. Apologise that you hadn't realised how hard this had been for them. Don't jeopardise their relationship with your dc and their aunt.
I know some people who really do take the piss with their parents and pils free childcare. One person i know slags off her mil for wanting to learn Spanish one afternoon a week (and therefore meaning inconvenience with childcare), saying to me huffily 'why the fuck does SHE want to learn Spanish anyway?' etc. It's really ugly.