Help! 5 month old puppy still peeing in house

Hi all, we adopted a 3 month old Aussie about three months ago and we're having a hell of a time with potty training. We take him out at regular intervals, about every 45min- hour. He is TOTALLY ok at night and when we leave and he is in his crate. He's also mostly ok when we're home except, According to my husband, when he's around me. The worst part is, he doesn't crouch, cower, nothing…he walks and it dribbles out, so it's VERY hard to catch. I have no idea what to do. The vet we were seeing said to pen him for longer periods of time, but as a puppy (and an Australian shepherd at that) I just couldn't do it. She very much made it seem like this is a potty training issue, but the dribbling is what gets me. My husband seems to think he favors me (I take him out and do a lot of active running and playing, I'm the one that does the more intense training), but I don't really see it in terms of "favoring" me. I have no idea what to do and this is just getting to be out of control. Some additional info:

• he is not our first Aussie, we're very familiar with the breed, but he is our first puppy -he did come from a shelter. We're unsure of the circumstances exactly, but the shelter staff said it was a "landlord" issue, so my best guess is someone thought a fluffy, merle colored Aussie would be super cute but had no idea the actual commitment, or needed to get rid of him asap, or both
• He was neutered before we brought him home ( 3 months post op) -we have three children (his "sheep") ages 9 and 5 year old twins. He likes to herd them, but apparently the accidents don't happen around them
• the only peculiar medical issue he has is his right pupil will dilate randomly (maybe just when he's excited?) It's not all the time and I brought it up to the shelter and another vet. We've been assured it's nothing, but who knows

He's definitely more protective of me, but not in an aggressive way, more like he'll get between my husband and I if we're snuggling and he has zero tolerance for intimacy (crate training is not coming along fast enough 🙄). I just don't get it…when it happens we're not playing, I'm usually occupied or relaxing, but he's also not trying to play in those moments, he's just moving from place to place, so it doesn't feel like it's for attention. We still take him out almost every 45 minutes, trying to teach him the bell, but it also seems like he's not fully emptying his bladder (which might be another issue). We live in western NY so he gets TONS of play time out in the snow.

It should go without saying but just to make sure it's clear, I've never hurt him or screamed or anything like that. We also have a great family, my husband and I are best friends and rarely bicker, kids are kids but we don't do a lot of shouting in our house. He's a really happy, amazing dog, and there is no indication he's going to pee when he does – it's a lot sometimes but he pees as he walks so it gets everywhere. I'll take him outside as soon as I see it and he STILL goes. I'm not convinced there isn't a bladder issue but my husband swears he only does.this around me. Any help is very appreciated!!!