What a horrible person. Doesn’t reply to your text messages; you can’t be sure whether he’d blank you (in your own home!) if you were to say a simple hello: and I have a suspicion he came off rather well financially in the divorce but has concealed this. He is continuing to manipulate you and you are (probably unwittingly) allowing it. For heaven’s sake, you are having tender thoughts toward him and don’t even know whether he’s in a relationship - and he is still so abusive in the same way he used to be, you daren’t even ask lest he ignores or lies to you! He even lies to your children about the relationship, and it has got to where they are discussing the photos in his house with you? Like with the food, he is using them to extend control over you. You must do the Freedom Programme, if you haven’t already. And you must make it a priority to find a good counsellor to, as PinaColada states above, rebuild your boundaries and help you see this situation for what it really is. There is no chance of this whilst he continues to take the piss and has you scared of being ignored, and hiding, in your own property, whenever he damn well pleases. The children do NOT benefit from seeing him exert this control, and have this effect, on you - be in no doubt they will have picked up on this and it will be hugely detrimental to their future relationships, whether you have girls or boys.
Do not think for a second that if you got back together with him it would not be even more miserable than before, because now he knows he can get away with any behaviour whatsoever and still you would entertain a relationship with him.
Step 1: starting immediately, he is not to come into the house (at least for a good few months whilst you can process Steps 2 and 3 below) AT ALL. He has the financial and intellectual means necessary, and the children are of an age, where he can make other arrangements. You are doing this for your children, so you show them how it is acceptable to be treated in your own home. That if you need to run and hide from someone in your own home, or they affect your mood and happiness, or you have to anticipate mistreatment/being ignored, they do not deserve to be in that home. Full stop.
You do not have to explain why to him. ‘The arrangement is not working for me’, via text. Change the locks. Really, change the locks.
That’s it.
To the children, as was said upthread:
Dad was unkind in the past and as a result, I’m finding it hard to continue as we are, so for now, this is what we’ll need to do, and you can still see and call Dad whenever you want.
Remember: this was and is not an experiment.
You are their mother, and this is your house. Your house, your rules.
Step 2: do the Freedom Programme. Preferably in person; if not, then online.
Step 3: find a good counsellor (don’t be afraid to reject one or more if she isn’t a good fit).