I'm not sure if it is a matter of emotional maturity but more of a deep routed mental health issue - I often wondered that with my ex P.
When I had told him that it was over - I cannot remember how many times he came up to me and said "So, this is what you want then"? or "Are you sure - this is on you - you can change your mind" - he had caused the pain and the abuse towards me and he was still looking for me to fix things.
When I didn't do my usual and cry, let him 'back in', he became quite nasty - or nastier than usual.
I think their ego's take a pounding and they genuinely have no idea how to even start to fix things. Mine said he would arrange counselling - but never did. Mine said he would do all sorts of things - but he never did.
If a relationship is valued, treasured and wanted by them, surely they would do what was needed to be done?
We do it, until we cannot do it alone any more.
Living in the same space didn't last very long for us. I was just a bit too hopeful on that one - there is no way that someone who cant do that in the relationship is going to be able to do that out of the relationship. They will get worse if anything because they just don't know what to do.
Keep your guard up and don't underestimate them.
As for telling your DC - age appropriate honesty is always the best way. Kids have this sixth sense when adults are sugar coating things and then they worry more. It may also be worth speaking to the school and letting them know what is happening so as they can keep an eye out and work with you if any problems crop up - I'm sorry, I don't remember how old your DC is?
Keep to routines and usual parenting styles - I had a friend that spoilt 'little Johnny' something rotten because his parents were getting divorced - no discipline, lots of treats, pocket money increased, chores forgotten about and both parents hyper indulged him - he was not a pleasant child at all and more than likely became not a very pleasant adult either.
My two children went through a divorce with me and their dad when they were both little - both grew up to be pretty decent, well adjusted adults I am proud to say.
I never bad mouthed their father, I kept to my usual rules and boundaries with them and I always told them what was happening rather than lie to them (age appropriate of course).
All our kids need is stability, love, safety and firm boundaries and values. If that comes from one contented parent rather than two unhappy ones, that's got to be a better upbringing.
Good luck and thinking of you during this wretched time - hang in there and it does get better eventually🌻