I suspect that other caregiver not changing the patient's diaper. What should I do if the husband doesn't respond?

Things changed appreciably for us when we did rounds in nursing report in patient's rooms. Report was given outside the room, then both shift's RNs entered patients room as a sort of "introductions". "Hi, this is Jean, and she is going to be taking over care for you for the next 8 hours". It worked well for patients, and gave the RNs a chance for a mini-exam. Included whether patient was clean and comfortable. Was a great change for all concerned. Might try this.

I suppose there is a possibility that the woman routinely lets go around the same time every morning, especially if she has been awakened by the night time caregiver checking on her.
The thing is that even if she has been left that way for an hour (or more) you have already discovered it's not going to do you any good to call her out on it, the husband is unlikely to want to go through the process look for someone else who may not be as reliable unless he sees signs of skin breakdown caused by neglect. IMO your best strategy would have been to have a private chat with the nighttime caregiver to try to work this out between you, but unfortunately you have already started a war with her. Perhaps you could ask the husband to allow some overlap of your schedule so that the two of you could both tackled the morning clean up together?
BTW, I have a relative who works in long term care and this happens in facilities too.

You have no authority to go out and by a camera & place it in the home, especially in the woman’s bedroom. If the husband isn’t concerned, there’s little you can do. You’ve informed him of the concern. Just do your job to the best of your ability.

I've been an in-home caregiver for many years. You probably have too.
Now, it's not my intention to be gross or disrespectful here, but people like us are experts on piss and sh*t. We know what a diaper and mess looks and smells like if it's been there for a while and not changed. If the overnight caregiver is saying she was dry for a half an hour before you came, well that a lie. A diaper that was changed 30 minutes later isn't going to weigh a ton and be saturated with piss.
As for the "things change remark" from the overnight caregiver. She's trying to push you out. She wants daytime hours or she has a friend or someone who's a caregiver and needs a job. She may even be planning on living there. You know the world of private caregivers is treacherous. If you suspect the husband will fire you if you talk to extended family about it, then you're going to be out of that job very soon. There's no two ways about it. The other caregiver is there overnight for 12 hours? That's a lot of time to work on someone. To give them a sad story or to bad-mouth other caregiver sharing a position. Talk to the client. She's 61 years old? Does she have Alzheimer's/dementia? If she's still in her right mind tell her what her overnight caregiver is planning. She might be afraid to say anything about out of fear that no one will take care of her. She doesn't need to fear.
You're getting thrown out though. I've had this happen on a couple of jobs. That's when I follow the scorched earth policy. Tell every family member who will listen what's going on. Report the neglect to every social service agency in your state including APS. Start doing this now. While you're still employed there start documenting everything and taking pictures of the condition the client is in when you arrive. Then take all of it to APS. They'll talk to you.

Obviously the first person to talk to is your boss -- the husband. This isn't about you needing to deal with a mess since it's part of the job, but it isn't healthy for your patient's skin to be sitting in that.

I can see not disturbing the patient as often overnight, but I know my mom's nursing home puts an extra pad in her diaper at night to keep from having to wake her to change it every two hours like they do during the day.

This can be dealt with without getting someone in trouble, but a meeting with the boss and then with the other caregiver is in order, so you're all on the same page.

Its not your call to confront her. You have reported it to the husband, who is her employer and he spoke with the caregiver. Her hostility maybe because you are right. But because you are privately employed, you have no right to tell her how to do her job.