I worry about the fact the commission model leaves me with too much liability, so I am looking for alternatives.
If you are going to train, commission for them only model is out of the question.
A nanny service is almost a commodity, there is only so much people are willing to pay, a lot of demand but not acquired by everyone. Your profit margins will most likely be small because essentially you are getting into a brokerage service for the nannies taking a commission off each placement.
Because of the low margins, you're better off maximum get each sale. Instead of making the primary business model based off 1 time hires/sales, focus on selling memberships... Try annual or bi-annual memberships that guarantees them a discount when they do actually hire, maybe offer faster or preferred services. This guarantees you operating cash flows month to month on top of the sales off each actual hire that pays for the nanny's hours worked and can give you an additional profit margin as brokerage commission.
Monthly + commission - (EBIT + Op. Exp)
Best business model is the one that works... You may need to try a few different things and test the market.
I have 1 recommendation on a specific model however. Schedule any consultation with me to discuss your options.