Finallyonboard yes, I think that is harsh. I think the OP is pregnant and has suspected pre-eclampsia, her mum has offered to help her and her dh look after her grandchild. I am not sure what you think entitled is, but I don't think it's that! But I won't put the boot in as you are off your high horse! 
I too have a huge interest in justice but I think this is more misunderstanding than injustice. Many grandparents may love to look after their grandkids and just not be asked. But 5 weeks is a long time.
She is worried and there seems to have been a misunderstanding about how things will be arranged while she is in hospital. I am sure it can be cleared up and I hope OP will accept how things play out. Although at her own home may be less stressful for the child being at Grandma's may be less stressful for the adult and stressed out adults don't mix well with young kids, so OP, please do trust your mums judgement if you think she is a good, safe person to look after your dd at your house, hopefully it will be the same at her houses.
I do not think you sound ungrateful, OP, I think you sound worried - and that will not help you.
You are lucky your mum has offered, I know my mum could not have done that for me and my dear in-laws in their 70s might have offered but may well have found it hard!