Not nice however you look at it.
One of my relatives spent years co-parenting children with a woman she actively disliked - her husband's ex. Her husband disliked his ex even more and found it hard to be civil to her. My relative found herself very often being a go-between. She felt that she had no option because otherwise their animosity ended up affecting the children - battles of dental work, sharing of holiday time and the like had caused immense problems for the children in the past.
The husband and his ex had different ideas on parenting (and pretty much everything else too). Each of them would have been very happy if the other could have disappeared and my relative would have been over the moon if the annoying ex would have gone away.
When my relative's husband died, she could have cut off all ties then. Her step children were grown up and she had no more need for contact with anybody in that family.
She decided not to. By then she and her husband had had 3 more children and she wanted them to grow up knowing their half brothers. So she swallowed her animosity toward the ex, invited her to the funeral and meets her very occasionally for coffee. They will never be friends but as they share a link through children that are no blood relation of my relative's, they keep in contact and remain at least civil.
My relative went on and found a new partner - her 3 kids now consider him to be their daddy. The oldest is 7 just now and the twins are 5 and there would be I think life long resentment if my relative and her partner ever split up and the partner were excluded from their lives. I have spoken to my relative about it and she reckons that she's very aware that no matter how things go between her and her partner, he is in her life forever because of his involvement in her children's lives.
I feel utter horror at the thought that my relative's partner and those children would ever be split up. I spend a fair bit of time with them all and the love that those kids have for my relative's partner and the love he has for them is so clear. I truly believe that the children and the partner would be irrevocably damaged if they were to be cut out of each other's lives.
I do hope that Matt can work through his anger enough that he can see the potential damage to your children and to Si (although he may not care about the damage to Si).