Single parent can't afford to rent based on income

I'm in the process of selling the house I own with my ex husband, I should ultimately end up with 300k. I've just started a new job where I earn around 55k (I know)I have 2 young children including one in childcare. In the city I live in there's very little to rent under 600 a week and that includes 1 bedroom places and 2 bedroom places even in unpopular suburbs. I won't get approved to rent these places as obviously this is more than 30% of my income, I'd like to buy again but not sure how I'll go with getting a mortgage with 2 dependents and a low income. One option would be to offer rent in advance but apparently this is illegal? My dad has also offered to help me, anyone have any ideas on if he can rent under his name but not live in it?? Is there a name for this type or arrangement? I don't want to do anything dodgy, dishonest or unethical but am new to renting.