These are the normal consequences of an unsupervised toddler.
They may or may not be acceptable to different people (parent / host) depending on their personal expectations and preferences.
Some people are clean freaks, some people are slobs - most of us are somewhere in the middle.
The toddler may be unsupervised because:
the DM is dissociated by trauma
the DM is lazy
the DM has a different parenting style / housekeeping standard
the DM is leaving her child unattended due to cultural norms where the expectation is other adults in the vicinity pick up supervision.
Or it could be a mix of all three.
It’s your home and only you know what level of consequences of an unsupervised toddler are tolerable to you and your household.
It seems there is a gulf in communication and mis match in expectations.
You need to calmly, gently and assertively and repeatedly tell the DM what your expectations are. Look in the first instance to resolve this tension by communication even if you know that this isn’t a sustainable long term arrangement for you.
You need to look out for trauma and if she is unwell then she and her DC need professional support - that’s not something you can shoulder - it would be unethical to do so - and maybe they need a different environment.
You have provided an open, generous, safe haven. If you can’t meet their needs (trauma) and the child is a safeguarding risk (unsupervised) then this needs escalating.
If it’s lack of clarification, issues on expectations then this can be worked on if that’s what you want.
Don’t get too hung up on the 6month commitment. That’s just the government saving UC rent money - if they have been with you a couple of months it might be better for them to find a long term solution sooner rather than later.
Many arrived maybe expected they would be returning home at the end of the summer. That’s not going to happen. I suspect many will now need to look at settling for the next 12 months - and I know the government will be looking at ways for hosts to extend the 6 months.
Its interesting that your DH doesn’t see the issue as you do. But that doesn’t invalidate your experience and is only likely to frustrate you further.
I am in a similar situation with respect to my DH - but he isn’t the sole contact 24/7 for all the guests issues, he is out of the house 12 hours a day at work and on hobbies - so I bear the brunt.
I took it upon myself to have an assertive and clear conversation which made me feel a lot better and improved our relationship because I was becoming resentful and contemptuous.
So my advice is to communicate - little and often - calmly, gently and assertively.
It’s tough.