she's not my child I find it difficult to assert any authority.
Ok let's unpick this....
I know on MN that it's generally advised that SP's neither "parent" or "discipline" SS.
Frankly I think that's a big part of many issues.
Straight away a dynamic has been created where the SP has no control within their home and children can and will act on that.
As a SM myself, DH and I agreed early on that we would have "house rules" that were applicable to everyone.
Simple things, like respecting people's personal space/possessions and privacy, keeping rooms tidy, being polite to each other, eating together at mealtimes, having basic age appropriate chores.
We also agreed the punishments for not adhering to those rules and they are enforced by DH or me (whoever is nearest to the action so to speak).
DSD and DS have always been clear that the rules apply equally to both of them and in the same way at age 11 I wouldn't have tolerated DSD jumping on me for fun, neither would I have let DS get away with it and also no issue with disciplining as necessary.
So many SP's end up in this awful situation of being powerless in their own homes and people wonder why they become disillusioned by family life and resentful of SC(s) when the issue is why wouldn't they be when the status quo disenfranchises them from the family in the first place?
To be clear that's not to say I get involved with "everything" re: DSD.
What we call "life decisions" are the proviso of DH and his Ex - so things like what school she attends, health concerns/treatments, when she got her ears pierced, advice on which Uni course etc.
That's not to say I don't give my opinion to DH on these issues, but I don't voice them to DSD and I also respect that the final decisions will be made by her parents (and would never criticise that decision even if I didn't agree with it).
So my advice OP is that you need to speak to your DP pretty frankly. This won't get better if your feelings and participation in family life are ignored.
You're a responsible adult in the home and parent or not entitled to enforce (previously agreed and communicated) discipline for behaviour that's unacceptable.