YABU OP. YANBU to want help but YABU to expect your DM to just become a single parent to a toddler indefinitely and just be happy about it.
Your DM has been left in sole charge of a 1 year old for 2 days, 1 year olds are exhausting when they're your own, never mind someone else's, and she's probably just tired and wanting to know when she is going to be relieved of this responsibility. Your DH needs to be spending more time at home with your DS - not just for your DMs sake but also for his sake, he's going to have a lot of adjustment with a baby sibling that isn't going to be helped by the fact he has been left without either parent for multiple days and he may start to feel jealous/unsettled which can manifest in challenging behaviours.
This will .make your DMs job harder if your DS is feeling unsettled and therefore isn't in their usual routine - you complain that she isn't putting your DS to bed until 10pm when you put him down at 8pm but it might not be an active choice, just that he won't settle at his usual time so she has taken the path of least resistance (after a long day of dealing with a child who is missing his parents) and let him stay up an extra couple of hours so that he will be exhausted enough to settle without either parent. It may even be that she's hoping your DH will be home by then and your DS can see him for a few minutes before bed.
When she was asked to help perhaps she expected your DH2 to be doing the bulk of the parenting and she would be there to keep up with stuff at home (cooking/laundry/watching DS while he runs to the supermarket etc) and only take over full parental responsibility while your DH was visiting you in the hospital for a few hours in the day. But what it sounds like is that your DH has spent the bulk of his time at the hospital and DM has just been expected to do everything and suck it up.
Being in someone else's house is also difficult - you don't know where everything is so stuff isn't to hand the same way, you can't truly settle and, at least for me, I never sleep properly in someone else's house. Not to mention she may not be sleeping properly as she's listening for DS and/or is out of her routine so that is adding to her exhaustion.
There's also a difference between babysitting for a couple of hours and full time care - even as a 30 year old with a 10yr old DD I find it exhausting to have my 1yr old niece for the day because I am so unused to the constant supervision needed by a toddler and the fact that she doesn't nap as well when she's being babysat and so is tired and cranky doesn't help either.
So whilst I can see it's difficult I don't think your DM is unreasonable to be questioning how long this is meant to be going on for.