Sybil's biggest barrier in terms of finding other avenues of useful, good paying work is her lack of education. If you recall, governesses are only good for learning French and how to curtsey and the Granthams never sent their children to school. So while she's bright and uses her mind to consider and make carefully considered decisions, if she wants to not just work in a factory, she will need to go and further her education first. If that's the case, can she and Tom afford for her to a) not look after the child and have to pay someone else to do so and b) can she afford the time to do the learning necessary to bring her to a point where she could consider for example going to medical school to become a doctor? Even if she wants to be a teacher, she will need to bring her skills up to par in order to learn to teach a class.
I think in 1920, once you become a mom, that is your job. You're number one priority. And I don't see Sybil going out of her way to search for a job beyond what she's already capable of doing or further her education. And frankly, I don't really see her being that upset about it. As most women, even the most forward thinking, progressive women back then didn't have an issue with being a homemaker. And Tom will provide as best as he can for the both of them. He'll make sure of it. And even though they'd refuse financial assistance from the Crawley family (beyond what they've already provided for her dowry), I bet you anything, they'd take advantage of certain 'connections' Violet or whomever might throw their way to ensure their sustainability. They won't be destitute.