I went so far as to allow visitations in my own home. My T mentioned that it confuses children and gives them false hope of reconciliation, when reconciliation isn't going to happen.
It can make for a difficult time, moving forward with your own love life. There's many drawbacks. It's eventually an illusion.
Many have done everything trying to give just one home to kids v. Two. All shaped by the major waves of divorces in the eighties. It's understandable, yet, it's not such a good set up. Plus teaches dependency, in its own way.

My scenario resulted in an assault after a heated couple weeks after my ex discovered texts on my phone from a love interest. ..

Divorcees need privacy. Even being friendly sort of, there's an underlying discomfort.