in this house we are a family - and that's how it works for most mums with a resident SDad.
Says who? What MN has shown me is that there isn't a "norm" or "most" - every single household is different 
We tried your approach - the one family, two adults, both fulfilling parental responsibilities for all DCs - it didn't work.
My DD (50:50, technically resident with me) doesn't consider my DP to be an equal parent figure; she is comfortable with him, and enjoys his company, but prefers to spend extra time with her Dad than with my DP if I'm not around for a few hours. She doesn't consider him my equal, and she struggled when I expected her to accept his direction, discipline and even praise!
My DSC's (non-resident) were unhappy about a single household model and it created stress, anxiety and emotional conflict for them.
Perhaps that was because, like the OP, their Mum was unhappy about it. She made sure that the DC's knew where her boundaries were with regard to my involvement in their lives, and they adopted those for themselves.
Everyone is far happier now we've stopped forcing things; I don't do DSC school pick ups except in exceptional circumstances, and formal childcare is the option that we choose to use rather than DSS spend time home here with me when DP isn't able to get home during contact time.
DP tells DSS to get ready for bed, put his shoes on, brush his hair; I do the same for my DD. If DP is cooking a family meal and DSS wants his attention or needs his support - then either I take over cooking, or DSS joins in with the food preparation. DSS would not be happy with me fulfilling that role, and I'm not going to force him to.