Car insurance of $100 a month seems high but if we exclude the car payment and credit card as things that we're obviously going to fix then you're looking at predictable monthly expenses of around $1300 of which $700 is building equity in the house. That's not so bad. That's your base level of unavoidable spending and given you have an income of $4000 post tax you're in great shape.
$6000 on the credit card is an emergency obviously but you can pay that off in around 2.5 months, 3 at most. I wouldn't worry about an emergency fund before paying off the credit cards, if an emergency strikes the worst case scenario is you just put the debt back onto the credit cards. I wouldn't delay digging yourself out of the hole for fear that you might get thrown back in, you need to pay that off asaply. You also need to change whatever habits got you $6000 in debt.
Cousin debt, see what you can do to buy yourself three months to pay off the credit cards first. Depends on your relationship with your cousin and how much faith he has in you. You still should be able to pay more than the minimums on the card, even paying $1000 to your cousin, but he's not charging 20% interest and the cards probably are.
Mother, same as cousin, if you can delay, defer or reduce the amounts in the short term without endangering her then do so because again, she isn't charging interest. Every $ you send her costs you more than a $ because you are literally borrowing money on expensive terms to send to her. Put it in those terms in your head and reevaluate the decision. It may be unchanged, if it is then so be it, she's your mother. At the very least talk to her about it though because you can't afford to give money away right now but you could reasonably afford to do it soon.
Car payment, downsize or pay it off asaply. You owe 22k and you pay 6k a year? How many years do you have left on it, what is the % interest on that debt?
In your position I would put 2k a month at the credit card debts, 1.2k at combined expenses and the remaining $800 between car payment, insurance, phone and hospital (assuming my mother wasn't literally starving). If she was then I'd put 1.6k to credit card debts. 3 months and those are gone, it's the start of April now so we're talking start of July to be credit card free, end of July if you're feeding your mother. You've saved yourself paying the interest on those and generated $6k of emergency credit to call upon if you had to. Well done.
Next emergency is the car. At 2k a month there it'll be the start of September before it's worth what you owe on it. That's really not so long to go. By Halloween you'll have enough money lying around to trade the car for a cheaper one which you'll own outright, no payments to make. Now you'll have no credit card debt, no car payment and $6k emergency credit to call upon. We've been paying $100 a month on the hospital bill for 6 months at this point too, I'm assuming that at some point that will be paid off but we're still good there.
At this point we've cut $800 from your monthly bills and an incredible $28000 from your debts and it's not even Thanksgiving yet. You're still earning $4000 but your expenses are around $1400 (before mother). You're now looking at being able to pay back your cousin around 2 to 2.5k a month rather than the intended 1k. We're aggressive about this debt because he's been a very good sport about you not paying him back since April so we're gonna do 2.5k a month. Your original schedule was going to take 6.3 months from today so you were going to finish paying him off in November 2015. Even though we delayed starting payments until the start of November we're still going to pay him off in just 2.5 months so you'll be out of debt to your cousin just two months late, even though you delayed it by six months.
That gets you to January of 2016. Things look somewhat different now. You're still building equity in your home, half of your monthly expenses are on the mortgage which are savings of a sort, and you have an overall savings rate of around 60%. You're maxing retirement accounts, saving money, investing in yourself and generally being awesome. Now we look at this to project a date.
http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/Around 12 years. Well done.