Jesus no you do NOT have to put up with this!
They are 2 and 4!!
So. You have recently split. You have given him the chance to have overnight contact- proper, parenting contact - and the feedback is that not only is he not up to the job, he is NEGLECTFUL and quite frankly unable to keep them safe.
This is what you do.
You email him telling him that as from now, you are stopping overnight contact, and if he wants to get it reinstated, he will have to take you to court where you will be pleased to work out a suitable solution and a means to ensure that his parenting is adequate and safe and a defined contact order which can reassure you. In particular, the reasons you are stopping overnights are:
- Safety. He is not adequately supervising them when in his care - for example, he should be awake and with them at all times.
- Neglect. Children report inadequate feeding/lack of feeding, using the four year old to take care of the toddler while he plays games, and punishing four year old if this is not done adequately.
- Emotional abuse. Being punished for bedwetting, regularly shouted at in an inappropriate manner.
You recognise that of course contact needs to continue and you support their relationship wholeheartedly in a safe environment. Therefore you suggest:
(e.g.)
- Saturday/Sunday daytime access to be worked out to a schedule, e.g. every Sunday, every Saturday, every other weekend for both days, whatever;
- Weeknight contact 1-2 evenings, dinner - whatever.
Keep a record of emails. And DO NOT send them again. It's dangerous - they are far too young to be unsupervised, and as for punishing for bedwetting - bloody hell.
If he takes you to court, say bring it on - I don't want to stop you seeing them, I want you to step up and realise that you don't have sole care of a four and two year old and act like they aren't there and play computer games. If you do, the court is going to hear about it. He'll either step up, or will simply accept it.
Does he actually really want them overnight? Daytime contact could just work better. Hint: it will CERTAINLY work better for him once he has a new partner, I'll bet...