I've been here for 14 years now. I certainly consider myself a feminist, just not one who thinks avoiding places that may challenge my views is the right way to go. Funny, for all the sand around here I'm not the one with my head buried in it like some people on this thread.
As long as you have proper documentation saying that you have sole custody of your children you will not have issues as a single mum.
As others have mentioned it's expensive to live here, so do consider your budget.
For those saying it's perfectly safe. meh. I've been harassed by men here as much as anywhere, and this is my 4th country of residence. I've been followed around stores, and attacked by a man in a parking lot with his dick in his hand. Someone tried to steal my car. I don't fool myself into thinking this place is perfectly safe.
However, it does offer my children the chance to experience multiple cultures. They have friends from all over the world, from all different religions and walks of life, and I think that is a priceless educational experience they wouldn't have if we were in my home country.
I love the focus on Science and Technology here, especially for women. Unlike Western society, Arabs believe that women are superior at STEM subjects, so the number of women in STEM is 60% as compared to 20% (or less) in the West. There is also an incredible focus on getting women to work, and while cheap domestic help does enable that now, there have been several laws passed to ensure that workplaces provide nurseries, longer maternity/paternity leaves, etc.
If you're the type of person who values exposure to other cultures and thrives on challenges, then this is the place for you. If you aren't, stay in the UK.