My DH and I have separate accounts. This has always worked for us. We are each responsible for our own parts of our household expenses and we divide things fairly equally. 

I will say that in your shoes, I would lay it out for DW like this:

"DW, I am no longer comfortable with our financial situation. I am going move my finances over to XYZ bank and leave our joint account where it is currently.  I will put $X per week in that account for your discretion. The rest will be used to make sure that our home and household bills are paid on time out of my account. I am also going to separate our credit cards. I know that you love your kids and I do not fault you for that, your caring heart is one of the reasons that I love you so much. 

However, as our children are now all adults, we need to focus on our future and our retirement. I refuse to work until I am 75 because our adult children cannot get their acts together. This is the only option that I can see to keep us financially protected."

Now- DW will throw a fit, even threaten divorce possibly. It doesn't matter if you want to have financial stability in your life. You have to be strong and put your foot down here and now. 

Stop enabling your wife. The only reason she can bail out her kids is because you bail her out. She's not being an equal partner, and her kids had to learn their manipulative, conning BS from somewhere.

You seem like a good man, so find yourself a good woman who will APPRECIATE the work and income you bring in, not just expect to be kept.

If you want to look at this practically, you need to eventually retire, and staying with your wife won't allow that. I've watched a very good family friend have to continue working well past when he should, and it caused him to literally get someone killed because he had no business doing the job he was doing. But, when your wife spends your money and doesn't care if you're on the street, it's hard to not work. 

So protect yourself because no one else in your life, and ENJOY the time you have with your family, not enabling hers.

How many different fathers do your stepdaughter have, if I may ask? Are they simply following along in mom's footsteps? It's common for poverty + lots of kids to be generational. And if your wife is still this irresponsible, her daughter's are just as unlikely to improve. They learned this behavior from her.

Your wife is the selfish one, plus she's manipulative and using you. A marriage is a partnership and your wife isn't holding up her end. 

I normally recommend marriage counseling before divorce, but I have a hunch your wife needs years of individual counseling and a shit ton of work on herself before she's even dating material.

Looks like you have hard choices to make. Either you continue to enable the enabler and nothing changes, you can never retire, and your resentment grows. Or you figure out a household budget that takes into account all expenses including retirement planning for you and your wife (excluding support for grown children). Since all bills are in your name, do not allow her access to any funds except for an allowance, and make sure those bills get paid in full and on time.

She'll no doubt be angry, so prepare for that.

I'm sorry you're in this situation. I couldn't live like that.

You are being used as an ATM and not treated as a cherished life partner. It's clear that your wife thinks she's got you right where she wants you and doesn't have much respect for you.

You need to talk to a divorce attorney ASAP to gain clarity and help formulate a strategy. Depending on the state you're living in, you could be looking at paying alimony.

Tell your wife she needs to get a job immediately. Then, cut off her access to your money. Close all bank accounts, and reopen ones in a different bank in only your name. Remove your wife as an authorized user on all credit cards and utilities, change all your passwords, etc. Reroute all mail to a drop box. Next, suspend luxuries like cell phone, cable tv, etc. Shock the He!! out of her, and tell her she starts pulling her weight NOW if she want to keep a roof over her head. Tell her you're done with the dysfunction, the house is going up for sale as you'll be downsizing (can't house freeloaders if there's no room, right?) so she needs to get her act together.

Your wife will shape up and start handling her business, or she won't and you'll know it's time to pull the plug on this farce of a marriage. Either way, you need to protect yourself and stop allowing her baggage to impact your home and your life.

 None of them receive any kind of child support as they have had a difficult time proving who the actual father is.  

If you were not supporting them and they applied for state aid, they would be asked to make the suspected fathers and the state would compel a DNA test. Unless they were picking up guys in a drunken haze, they have a good idea of who the father is. DNA tests do the rest.

As to the four dropped off kids, wife and you have no legal rights. What happens when these kids need to see the doctor? You can't even legally sign a report card. Call children's service and report them as abandoned. Get  legal guardianship or a foster designation. In many states there are kinship care services you can access and medical.

There is no common ground. There is only what you are willing to tolerate.