This is the most tragic thread I have ever read. A mother of 2 very young dc is unwilling and unable to protect herself and her dc from an abusive wannabe killer husband.
He has just attempted murder and is sorry. She does not want to ensure her dc's safety but wants to keep them in a volatile and violent environment where her dc grow up thinking daddies strangle mummies but it is ok .
FFS op if you cannot and do not want to protect yourself you do realise by not logging anything with the police you are exposing your dc to a terrible and miserable childhood where by they will see dv as to be expected, your dd will be more likely choose a violent partner and your ds is more likely to turn into an abuser.
There might not be another time. Women get killed every week in instances just like this. Your failure to ask him to leave or call the police is the same as giving him the green light to treat you like this.
You are saying please do that again as by strangling me in front of the dc is ok, life goes on as normal.
By not doing anything you are saying to your dc this is normal behaviour, daddies can strangle mummies, it's ok.
You know it is likely he will do it again as your inaction gives him power over you.
You don't deserve to have your dc as you are not protecting them. By not protecting them or wanting to protect your dc from a violent and abusive home social services should come and take your dc away from you ASAP.