YABU overall.
YANBU to find being a stepmother hard, and it is upsetting when you are trying but not getting anything positive back. YABU about the rest.
Ultimately, you and your DP chose to be together. Neither set of DC chose the step-parent, or the situation as a whole. They have had the step-parent thrust upon them, regardless of their feelings or wishes. They are either living with an adult they may or may not feel happy, settled or emotionally safe around (irrespective of how you feel that you should be viewed by them), or are mere guests in their parents home when they “visit”. That goes for your children, as well as your stepchildren. It is unsurprising to me that many children don’t react well, for a whole variety of reasons- doesn’t mean that truly bad behaviour does not need tackled, because of course it does, but that has to be done with understanding and empathy.
Add in parents who are at loggerheads (regardless of who you believe to be at fault for that situation), and at least one parent who stirs things up by being critical of the other child parent and is manipulating a small child into thinking badly of them and their step-parent. And, then you say mum smokes weed in front of her children and does not work- suggesting at least a strong possibility of a somewhat chaotic life at home with her mum. I am absolutely unsurprised, given all of that, that you have a confused, unsettled and probably very insecure and unhappy little girl. Imagine how it feels being her, right now! Perhaps, use that to temper you irritation.
A child should not be grateful for having their basic needs met- things like having meals made or clothes washed. The adults they live with absolutely are responsible for meeting those needs, and that is not dependent on their behaviour being satisfactory. You were highly unreasonable to react as you did, and say what you did. I’m not saying I don’t understand why you might be frustrated/fed up/ annoyed/upset that your partners children have not warmed to you and don’t treat you particularly nicely- I do, and none of us are perfect. But, all you’ve done is confirm all the things her mum has been saying about you are true.
It might not be your responsibility directly, but if your partner is leaving you to pick up extra work for his DC, and you are resentful of this (which is justifiable), then you need to address that with your partner, not take out your frustration on a little girl. Even one who is not behaving perfectly. How would you feel if your DP reacted to one of your children they way you blew up at your step-daughter?
If you, as an adult, cannot control your temper when provoked, perhaps you need to give your DD a bit of Grace too? She is, according to you, being manipulated by her mother. You need to tackle behaviour with your DP, and work together to improve things.
incidentally, if their mother is as bad as you are making out- openly using illegal substances in front of young children, parental alienation (and lord knows what else)- why has your partner not tried to get full custody or things out in place to protect his children?