You need to set boundaries on this CP, for your own peace of mind and for the kids. It will only confuse them more if he keeps coming and going as he pleases.
The night my H initially moved out I took S13 to the drive-in, leaving my dad at home to keep an eye on what was being taken. H only took some of his clothes, toiletries and his computer at that time, so there's still quite a bit of his stuff still at the house. He is in the process of arranging storage for some of the stuff and then he'll be removing the rest of his stuff.
When H moved it was agreed that he would give at least 24 hours notice of intent to visit S13, and I had that included in our separation agreement as well.
It will probably be so much easier on you to be scarce - even if you just go into your room and read or something. It'll take a while before you're able to control your emotions - it took me several weeks and even now I still struggle once in a while.
Stay strong. Keep your focus on yourself and those kids of yours.
Both 50 S14 M 16 yrs (his 3rd; my 1st)
ILYBINILWY - 24 Dec 2012 H moved out - 27 Jun 2013 Legally separated - 6 Sep 2013 Closing the door and changing the locks