Some thoughts about the emergency fund:
First, since you are a single parent, I think the emergency fund ought to cover 6-12 months of expenses, rather than 3-6 months. Since you don't have a second person's income to buffer the fall, and you have children depending on you, this seems wise.
Second, as for using the ROTH IRA as your emergency fund - it depends on what you are invested in. To my mind, whatever part of the ROTH you are considering your emergency fund, needs to be invested in emergency-fund-type investments - i.e. safe investments, not stocks etc. The reasoning is this: sure, many emergencies that might befall you could be market-independent, such as a serious illness in the family that requires you to take prolonged unpaid leave. Extra disability insurance for yourself might be a very good idea, since your kids depend on your earning capacity. BUT - one of the biggest challenges you might face is what happened to many people in 2008 - a severe market downturn resulting in job loss at exactly the same time as the stock market goes south. You DON'T want to be forced to sell your market shares at the bottom of the downturn just because that's your emergency fund.
I'd say, figure out what you would need in addition to unemployment to get by on a strict emergency budget (let's say $1,500 a month plus unemployment for the sake of this example), multiply by 12 = $18,000. Keep $3,000 or whatever you're comfortable with in your ready cash, then keep the remaining $15k in your ROTH in a money market account. That way it would always be available even in a depression (although, sure, it wouldn't grow as fast, but I think security has to take a higher role in a single income family). If you lose your job but are getting unemployment, you're covered for a year's expenses; if you have to leave in some way that doesn't get you unemployment or disability payments, you're still covered for about 7 months of expenses.