Rules in a house should be made jointly. Disciplining decisions should be that of the parents. Ideally, the two should match but it doesn't always. In that case, it is about compromises, but ultimately, when the parent is present, they should take on the disciplining rather than living it to their partner to do.
What I often see is the parent not agreeing with the rule of the SP, but going along to avoid conflict. This means that they leave it to them to impose the rules, resulting in the child rebelling and the parent not supporting the SP because ultimately, they don't agree or are not bothered by the rules that the SM wishes to impose.
When OH and I got together, the first thing we discussed after realising that we were definitely compatible with each other was whether we were also compatible with our views on raising children. From my perspective as a mother, no way was I going to accept any new person in my kids' life (who they didn't pick) to dictate how I should raise them. Similarly, my OH was not going to share his life with someone who didn't respect rules that are essential to him for his happiness/well-being, so somehow, we had to have quite a similar perspective on it.
Thankfully we did. Still it is not easy. Cute kids become monster teenagers and dealing with them as a parent is very different to dealing with them as a non parent, mainly because however much they annoy, frustrate, disappoint you, as a parent, you are still able to love unconditionally. This is not the case for a SP. My OH finds my teenage boy very difficult at the moment and I can see why. I can also see why my son feels unloved by him. What helps is that my OH best friend confided in him that he was having difficulties with his own son (who is a year older) so helped him realise that it wasn't just SP who struggle. However, I am grateful that he has chosen to ignore my DS behaviour rather than confront him and trust me when I say that that period will pass and things will get better.
OP, speak with your OH and reach a compromise in terms of what minimum manners you both agree should be adhered to and then let him do the disciplining. It will always be much better received if it comes from him. That of course when he is around, if you are with him on your own, it should be clear that you are then in charge.