Are you sure lots of Eastern European women with children are leaving them at home to come over here? Undoubtedly there are really poor areas in EE, but in general, even in the poorest countries, there are some benefits/state accommodation of parents with children/state education/healthcare service and people are in general, not that dissimilar to many Western countries. There are very poor services for those with mental health problems, but they are not coming here to work; there are also communities such as Roma which are poorer than the average non-Roma person in those EE but again, I don't know of any working long-term here and leaving children behind them, they have freedom of movement and tend to prefer to move as a family, like most immigrants.
There is a huge youth drain in EE countries as the young twenty somethings come to Western countries (not just UK, Germany, France, Canada) and get jobs- and yes, typical entry jobs are cleaning and care work, as they don't require quals. I know lots of well-educated degree level EE single people doing these type of jobs.
My cleaner is not from EE but another European country with a high unemployment rate, she only came to the UK less than a year ago and loves it here as her business collapsed and within a couple of weeks, all of her family (her, father, older dd) have found work as cleaners and as a bar manager, they think the UK is great in terms of mobility/employment opportunities and already the dd has been promoted at work, so they are happy to pay the bills/have jobs again.
Is that exploitative? Capitalism certainly hasn't favoured them, but personally I think they are enterprising and sensible people who have done the best for their family in the circumstances they find themselves in. I don't know anyone leaving their children behind, I know lots of immigrant families and when they move, in general the whole family comes and benefits economically, as whilst one is working as a cleaner, they may also be studying quals/training/another gets a more professional job.