If you do go with 3B, you'll need to have a contingency plan in case she tests positive/doesn't test/otherwise screws around with SoberLink.
And while SoberLink is great for allowing safe visits between a child and an alcoholic parent, it also saddles the non-alcoholic parent with the job of monitoring and surveilling the other parent. Plus it can be expensive - unless your ex agrees to pay for it, you're probably looking at a couple of hundred dollars a month in addition to the up-front cost of the device.
If I were in your position? I think I would
a) take the government job - because you're probably going to be the primary if not only parent for your kid, and flexibility (time off as needed) is an absolute godsend (says one who knows). And given your age, life insurance and pension (with the kid as your beneficiary should you pass away) are a really good idea;
b) sell the house as-is, even with the financial hit. For me, the time and emotional effort that would go into fixing the place up for sale added to the uncertainty of selling the house at some future date would cancel out the potential additional $10K, especially if I took the government job and so my long term financial concerns were lessened. But I am extremely risk-averse and your mileage may vary. (And if it looks like the financial hit from the ugly-homes people is going to be bigger than expected - very little equity or negative equity - then you could consider taking out a line of credit and fixing the place up to sell. But if it were me, I think I'd try to sell it as-is first).