Living in the UAE as a single mom shouldn't hinder your teaching prospects. It might make immigration admin more stressful, and you should expect local curiosity about 'where your husband is'. You might be able to find some blogs which detail 'single mom experiences in Dubai'.
Teachers are highly paid in the UAE and, at the moment, salaries are untaxed. There are other benefits provided, such as accommodation and health insurance assistance. Getting reduced fees seems to be common, but it's unlikely that you can get full tuition as part of your package. This is part of your contract with the school and degrees of negotiation exist. Despite high teacher salaries, international schools in Dubai are prohibitively expensive.
It's also increasingly difficult to find employment in international schools in the UAE, as many international schools are starting to require their teachers to have Masters degrees. Thankfully a lot of schools have recently opened in the UAE, which is great for finding placements.
Have you considered teaching in any other UAE cities, like Abu Dhabi? By widening your search, you may increase the chance of finding that 'perfect deal'.
You might find this Expat Arrivals page on Education and Schools in Dubai helpful. And this page on International Schools in Dubai.
As a last thought:
Be careful of scam schools that offer too-good-to-be-true deals.
Hopefully, some of this is valuable.