You shouldn't have as many issues as a single mother with only 2 children, as I have being a single mother of 4. I've had a RE tell me 'no one wants to rent to a single mother with 4 kids'.
I have only tried once to get private rentals since having DD3 & failed. But that was more because there wasn't much on offer at the time. I've been in public housing since & am hoping to buy so I never have this issue come up again.
If I returned to that area I know I'd struggle. It was a struggle to find a long term rental with only 1 child & a partner.
I think area is everything. Although I haven't had an issue obtaining a rental, I do pay a lot more in rent than a lot of other places. I'm looking to buy also for security for the kids and myself. The amount in mortgage, council rates, insurance, maintenance etc is still less than the rent I pay now I didn't think anyone would offer a loan to me as a single parent but was pleasantly surprised, my biggest hurdle is getting the deposit and costs together while paying astronomical prices in rent! Don't let being a single parent put you off or stop you, its sometimes harder, but its doable.
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