Do you live in a really small state? Just asking, because in Oregon it would be impossible to be at one end of the state and back in a work day if you're driving...
There are a lot of factors. You have a young child. Working far away while they are in school/daycare can be difficult unless your spouse can easily go pick them up if they get sick, etc.
How much would you save on clothes? Would you save more money because you are home and able to start dinner on your break and not tempted to just grab something on the way home? Are there other current habits that could be broken in order to save some money?
Is your personality such that you could handle the isolation? Would your job allow you to work from anywhere, or would it have to be a specific place? (the paper work I've seen for the jobs here pretty much state that you have to be in an "approved" spot, where someone could come randomly inspect to see if you are there with only 20 minutes notice, etc. So, you could not take your laptop to a coffee shop or local park, etc.)
If I didn't have my current job, I'd love to work from home. There is no work-from-home option for my career though (it's hard to physically do a job or handle the emergencies if you aren't physically on site, some days I don't even log onto a computer).
Would you be able to reduce child care expenses? (If you can't just have the child alone while you're working, could you pay a neighborhood tween/teen a few bucks to come hang out as a "mother's helper"? They can do their homework, have a snack, play with the kid, etc, and you'd be there "in case of bleeding and broken bones".)
You say you'd have to start at the starting wages, how long would it take to receive a raise?
If I had safety concerns outside of my control, and could find ways the change would save money, I'd take the telecommute. But ask for additional vacation/sick time first.