House training

We are at our wits end with a 10-week old doodle who piddles without warning. We have followed the usual suggestions of taking him out repeatedly, using the bell at the door, scheduling food and water times, etc. We take him outside where he piddles, then he does so again shortly after coming back in. Yesterday I took him out to piddle but he ran back inside while I was distracted by our other dog. As soon as he got in, he piddled on the carpet. He completed a course or two of antibiotics for a UTI. Anyone out their have any ideas?
Mike