Hi, I also disagree with the suggestion you simply have to do as her dad does. That is a recipe for disaster once you have your own children and ultimately you have to get some agreement in your own home.
I have to say though that your assertion about showing respect to elders just because they are older is not really a viable parenting strategy. I have met as many idiots who are older than me as younger than me! Her teachers etc will give her reasons for asking for decent behaviour (e.g. we don't push BECAUSE blah blah blah, we don't shout out in class BECAUSE blah blah blah) so you are a bit out of step generally with the respect your elders thing.
You should expect general courtesy etc as a norm of course, but actually I think kids are programmed to test boundaries and it is by having consequences when they test that they learn. A child who never tests any boundaries and is simply 'respectful' the whole time is odd IMO.
So, you need to agree a set of house rules (either just with your DP or, IMO, also with your DSD too - altho that bit can be stage managed after your and DP have agreed in advance) and the list of consequences for not doing things. When my SS first started school, he became a nightmare for arguing with instructions. So we had a house rule that if it was an instruction, we said - 'this is an instruction, I want you to do X, y, z' and if he argued, he got a warning for arguing, then a consequence. He soon learnt... and moved on to a new way to drive us mad...
Usual parenting advice is to identify the behaviours you want and a reward system and the behaviour you don't want and a consequence system. Then if you and your DP stick to it you will make progress.
The issue comes really if you have a DP who never wants to punish/give consequences even after you have agreed stuff like this.
But I do sympathise - I became SM to a child of similar age and it is a big shock to the previously childless! It was a very steep learning curve. Good luck!