Sorry you are feeling put upon and perhaps burned out @Slickholly
It seems fairly standard for Ukrainians to leave their children alone at a young age - and it has caused problems for many hosts in my experience. (I've seen Ukrainians themselves posting about this often.) Perhaps they therefore don't think that you are doing 'childcare' for them when they go out? Because they would just leave the girls anyway whether you were there or not?
You don't have to go along with it. Tell them, NO.
From day 1, our guest left her child (age 8) roaming around our house while the mum was up in her room on her phone. With the door shut.
I felt like she just dumped the kid on me, but I don't think she saw it that way. Maybe because they had lived with grandparents in Ukraine and she didn't realise how much they were actually supporting her and the child. I don't know.
It was like I'd become mum to the mum, if you see what I mean. I found it hugely presumptuous.
There was very little personal interaction with the child. Days on end of phone time. Certainly no playing. Mum didn't know how to play.
😓 If that's the level of interaction expected while looking after children then it might seem like no imposition at all to leave them with others.
After one unfortunate incident where a neighbour's property was nearly badly damaged, I laid down the law that the children must be supervised at all times. We made a big thing of it. We had a family meeting with our guests. We spoke about it. We talked about our rules. We all learned how to say 'Stop it' in Ukrainian.
She did not then supervise her child.
The communication failed, in my opinion, because the mum did not know what on earth I was on about. Not the words, the concept of supervising children. She saw no need.
From that moment on that I never left the children unattended, for the safety of my own kids. I would not have my children shoved, pushed, bullied, missing out on treats because they got snatched away, following guest child out of sight in busy city streets etc, etc, etc.
It was exhausting.
It was exhausting work which could never be recognised by our guests. To them I was bonkers and overprotective and horribly strict. I was so f*ing glad when they left after 6 months. It took me the same time to recover from the strain of it all.
If your guests are not 'getting' your rules try making the rules very simple and clear:
One of you must be with your children at all times.
They may not understand it or like it but you can tell them that after being left with the playdate you need absolute clarity and no room for misunderstandings.