What is the process for remarried couples to convert to Catholicism?

I was reading and trying to understand [_Amoris Laetitia_](https://en.m.wikipedia.org/wiki/Amoris_laetitia) and came up with this question below. The documents talk about irregular couples and basically say that everyone undergoes different timing of conversion. This is a situation: A non-practicing Catholic couple "divorces" and re-marry by state. They end up having families, let's say with 3 or more kids with another husband/wife. According to the Catholic teaching, they live in adultery. Now, they start to be interested in spiritual life and undergo what we call a conversion. But they are stuck because they can't just split and leave their kids or whatever dependencies they have. I know the ideal would be to get an annulment and solve this problem. But let's say they aren't entitled to an annulment. My question is what does the church offer to such couples as a solution? Suggesting to live like a brother and sister isn't going to work unless they stop living in the same household but that might not be ideal for kids (I guess) or it can still cause a scandal. Is splitting couples really the only way to go if they want to live a sacramental life? I know this happened to St. Augustine but his situation wasn't that complicated. Do we have other examples from the past where families needed to separate in order to return back to living in the state of grace? Have Catholic theologians written on this subject and if so could someone explain it to me?