I think you need to consider which route will maximise your chances of success, given your background and experience.

Government job is fine, but the environment is designed for scholars to win. If you're not an overseas scholar, there will be a ceiling for your career progression. If you don't mind the slow and gradual increase in salary, and value certainty of (relatively) low pay compared to your scholar peers, then it's a good route to choose. Limited career progression, will struggle to be "comfortable", your kids will probably still be caught in the poverty cycle (slightly exaggerated).

The private sector feels like a better option, although your background may make it difficult since you will be competing for jobs with the local grads (NUS / SMU / NTU). Not to say you can't make it, but it is an uphill battle because you need to overcome the market prejudice of a SIM degree (in some firms).

Why not even the playing field and try being your own boss? Can be real estate agent, or financial adviser. It is a purely sales-driven job, where it depends on how hard you are willing to work. Grads or not, scholar or not, there's no advantage. Downside is you actually have to work very very hard, and that earnings at the start could be uncertain, but the upside is tremendous. Given that your alternative to earn $3K-$4K in 2-3 years' time, I think the opportunity cost is relatively low.

That's what I would do if I were in your position. Hope this helps.