ETA: I see your update. Basically, this isn't about her or the guinea pig so much as you simply don't trust him. So if you don't trust him, you can do a couple of things - stay, and learn to trust him or stay and be paranoid about his interactions (including this woman with whom he has a child and must interact with) or go and find someone you do trust. If he won't go to counseling you can go by yourself to get a better handle on the situation, regardless of what steps you took. Frankly, what kind of a relationship do you have if there is no trust and no willingness to work on it?
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I would talk to him further about boundaries in your home and what you feel is appropriate and why and vice versa. I used to have my DH's ex making herself at home in his (then later our) home. Used our dishes, left trash, pulled out our board games to "wait out traffic" when neither of us was home. If your DH was home to supervise, that's one thing (even if you were away) but if she lingered when she was just doing a pickup, that's another.
No matter how flirty SHE is, you only worry about his reaction to it. She could be anybody and you either trust HIM or you don't. My DH said his ex used to wear this one dress she obviously thought was super sexy, til he joked that it reminded him a of a particular cartoon character. She never wore it over again. I was never worried about HIM wanting HER back. But I didn't trust her not to snoop, and that was hard for DH because he saw it as "the kids have a guest/it's easier this way". Wasn't til one of his coworkers reacted strongly in my favor that he realized he wasn't looking at it from my POV and took steps to stop the pit stops in our home.
If the issue is that you want to know when she is there, especially longer than a pick up or drop off, then ask him that, and only if you really think it's important. And if you think it IS important, why? Because of her or him?
My DH allowed his ex to see SD's room when she repainted. The ex forgot what room was SD's and went into SD's old room (which had become the nursery) and he says she recoiled. So sometimes, joke's on them.
And I used to get really irked about a lot of things I no longer get riled about. Some of it is that I now feel heard, some things changed and some things are truly small potatoes. I just had to get to that point of understanding. So think about what is a hill to die on and what isn't and go from there. And hard as it is, try to separate the child from the mother's behavior. Was it an issue because SHE wanted to see the guinea pig or because the child wanted to see the guinea pig?