You are entitled to your feelings, and to have a moan about it but at the end of the day- if you get into a relationship with someone who has existing children then this is always a possibility.
Whether that be through death, ill health, or just the inability to be a parent from the other parent.
I actually know someone this happened to, she was actually the OW. Naturally she was okay with the child of her partner coming EOW, which is pretty standard when relationships end.
Very tragically, the child's mother was diagnosed with a terminal illness and died at a very young age. The child was only in reception, and had to come and live with Dad and his new partner full time. It was a huge shock to her, something she never considered and she was hugely resentful for years. She wanted to have her new family with her DP and never considered his existing child may at any point become a permanent fixture.
The DP has a high paying job, so it was agreed after a while for her to give up her job, get married to the DP (for her own financial protection) and raise her step child and their own children full time. I think this helped with her resentment as she quite liked being at home. (IMO the Dad should have stepped up and been the default parent but they seemed happy with this arrangement in the end).
These things do happen, and I think it is quite silly to get into a relationship expecting that it would never be a possibility that your DP existing child/or children may have to live with you full time at any point.
There's been a few posts on her recently when teen step children have had to go and live with the fathers for various reasons, and step mothers complaining that the house isn't big enough and of their own DC having to share or give up bedrooms etc.
IMO both mothers and fathers shouldn't be creating new families or more children when they haven't got the means (including enough space/bedrooms) for the existing ones. That's in an ideal world though!
In this case your only option is to either leave if you are unhappy, or get your DH to fully take on any responsibility for your step child (this may cause issues for her though if she feels/unwanted or not fully part of the family).