My 3 year old Yorkie-Poo is using the bathroom in my house!

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I have had my Yorkie-Poo for 3 years hes not a baby anymore and i walk him over and over and he likes to go to the bathroom when he wants i take him to all his spots i even change it up at times and walk him longer to stimulate the bowels like the vet told me and sometimes he wont bother to go because he is so nosey looking at other things. I try to use commands to make him go and still nothing. I punish him by giving him a time out in the doggy cage when he poops on the floor. I get so frustrated when i come out of the bath or the bedroom and there is a pile somewhere. are these dogs the hardest to train? when walking him he likes to do the puppy thing pulling away doing some kind of weird jumping to get to a certain spot and its not like I'm not walking him fast enough because i am. I just wish he wouldn't make a mess in my house. I clean my carpets so much i have kids and cats and they don't even make as much mess as he does. (the cats that is LOL) I sometimes stop at neighbor's house before coming home and if they invite me in i have to leave him on the patio because he likes to pee against there trash cans and furniture? well when hes home he acts like he wants to pee at my trash can too and on my bathroom floor and sometimes in the middle of my living room.