Yeah, I understand about your wishes not being respected on top of more lies. I'd be pretty well P.O.'ed myself. And, for the record, I wouldn't let my XH's GF in the house for a long time, but they got involved while we were still in MC, though I doubt she knew that. Oddly enough, they both helped me and H pack the house up when I moved.
Does your H have partial custody of the kids? I would think having any custody would mean that he should be able to cover food, shelter, and clothing for them. Otherwise, wouldn't he be an unfit parent? Wouldn't your child support payment be higher if you had full custody? He needs to buy them some freaking clothes. What a creep.
I guess I asked about GF not because I thought it was OK for her to bring the dog over, etc... It absolutely wasn't. But rather because I was wondering if that was really a battle you want to fight. STBX will lie and manipulate as long as it is easier for him to do so right now. There will be less reason for him to do so if he doesn't have to worry about managing you with respect to his GF, if that makes any sense. Maybe if he feels like he can be more honest with you, things will get to a better place, which would be better for you and the kids.