I'm a step-mum to 2 (now grown-up) and a step-nan to 2.
we had a few drama moments in the first year, almost exclusively down to my lack of understanding of how to do things - I tried telling them off, rather than setting boundaries but asking DH to enforce them. They pushed back as it was 'their' house, and played their natural parents against each other ... the usual stuff, really.
15 years on, I love my children dearly, and I know they feel the same. I acknowledge I will never be their mum, so - as another poster says - I try for an 'aunty' role, which works really well. Mind you, to the grand-kids, I am "number 1 nan" as I put the time in, so I think the lack of biology gets trumped over a generation by love.
The best advice I can give you, OP, is to pour a glass of wine each evening with your DH/DP, after the kids have gone to bed, and talk things over rationally, laugh, vent, cry, whatever - but do them together and don't let the kids see. Face everything together with 1 position, even if you disagree privately afterwards. Never slag of their mum, stay silent if you cannot say anything nice. Invest, and you will reap.