Schengen regularisation

I am an EU citizen, working in Malta (with residency permit), but for my mistake I didn't take the residency permit for my wife, which is not an EU citizen, and we have been here for 9 months now.
We have a baby which is breastfeeding, Also our baby have EU citizenship.
I am trying to find a way to regularise my wife's situation, but all that I can find is that she must leave Malta as soon as possible with an almost certainty of being banned from entering Schegen countries for 5 years.
I would like to request your advice on a way her situation can be regularised without she being away from our baby, and also without risking bannement from Schegen countries.
I work, I pay taxes, we have private health insurance, she never used Malta's public health system. In some years she will become an EU citizen.
We just don't want to live in a situation where she feels unsafe because we can't find a way to regularise her situation.
Thank you in advance for all attention to my enquiry.