You are absolutely correct. You are not responsible for someone else's kids. Financially or otherwise. I would never expect a significant other to be responsible for my child in any way. 

I am the breadwinner in my house and I do not contribute to SKs financially and I won't. If they get anything from me it's a gift from the goodness of my heart nothing more.

Just because I can afford to give things to DS SKs parents can't is not my issue. Because they actually could if they wanted to, they just choose not to do better for themselves or thier kids. My parents went back to school and didn't start Thier careers until they were in Thier 30s anyone can do better for themselves at any time.

You're correct in that you're not obligated to pay for your GF's kids in the same way that you pay for your own (or at all). However, I want to address some other problematic behavior that was brought up in your post.

Primarily, people like your GF get created because of people like you. Someone else is willing to take care of them, so they have no reason themselves to do what needs to be done.

In the case of your GF, I am wondering how you two met. You say she doesn't work, and it sounds like you may not need to. Did you purposefully seek out someone who wasn't working so that you'd have a companion that can travel, go do activities, etc? If so, then the flip side of that kind of freedom from a companion is responsibility for them. It's very rare to find someone who doesn't have to work that can still fully support themselves, especially if they have kids. I'm not saying you have to support your GF, but unless you really narrow down your search of free partner with their own indirect income, this is the type of situation you'll continue to find yourself in. And a partner with financial AND time freedom is hard to come by.

Now, we have to look at your daughter. Like I said, people like you create entitled people. Yes, your daughter may struggle, but she has also made some very adult decisions to have kids and get married. She has some responsibility to pay her own way and not feel entitled to have her parent pay for her to survive. There are better ways to share your wealth - offering a down payment in a house, setting aside college money for the kids, covering a family phone plan that includes her and her FH, offering an annual gift - that helps but doesn't enable. 

Basically, you're crippling your daughter. She has no reason to try very hard because her parent will bail her out. My BIL is like this; his entire existence is paid for by my FIL. Anytime he talks about his car, he says "we had to buy X for it". No dude. FIL had to pay for it; you didn't pay squat.

So, if you're going to be critical of your GF having gold-digging habits, you need to be giving a critical eye to your daughter and her situation, too, before you end up supporting her for eternity.

This now leads me into my next point: your son's paternal grandparents that he lives with. Are you paying child support to them? They are "doing your job" by allowing him to live there, and it only makes sense that you'd be giving them at least close to what you give your daughter. Even if they don't "need" the money, it needs to be paid. It's a responsibility you have. Pay them if you aren't.

And finally, switching gears a bit, you're a bit wrong in your assumption that your GF should have no say in how you spend your money on your kids. If your GF is a serious relationship that is going to turn into her becoming your spouse, or spouse-level should you choose to never remarry, you two will need to discuss finances for the health of your relationship. Being the person with money doesn't mean that you unilaterly get to make all the money decisions. By becoming an equal partner with your spouse, you open up those parts of your life to them.

Now, that is NOT me saying that you owe her half of your inheritance or should pay for anything she asks. That IS me saying that you two need to discuss how finances will run in your family. I go back to Point #1: if you want a partner who is free to do things with you AND you choose someone without their own indirect income, then you've sorta set yourself up to pay for their livelihood, and in relationships like this, you take on their assets AND liabilities. HOWEVER, paying their livelihood doesn't mean you control all the money in the household. They are an adult who has mutually chosen you, and the two of you need to be on the same page about how money is saved and spent in the home. 

If this is not an arrangement you want, then you can either dump your GF to find someone with similar income and freedom as you (likely very hard), or keep things incredibly casual with your GF, including having her live in her own house that she pays for.

Why are you supporting a bunch of grown-ups who should be supporting themselves? Ie, your kids and your GF?

 She's wrong to expect you to support her kids, but stop supporting her and your kids too. If your 20 yo is old enough to make two babies and get married, she's old enough to work to support them as well. And as for your GF - what kind of self-respecting adult wants their partner to pay for everything for them?

Seems to me you are being used by many of the people in your life. Would your GF stay with you if you stopped supporting her? Time to find out.

You are not obligated to support her.. or her children.  She is an adult.. she and her EX created those kids.. she should be able to pay her own bills.. and if her kids need help.. she can help them.

So. no you don't have to give anyone money that you don't want to.

And.... I'm going to take that further and say "including your daughter and her fiancee"  How long have you had to help them and why do two adults need you to almost fully bankroll their life?  I am speaking from personal experience when I say that when kids are overly helped by their parents (or other relative).. they become dependent on the help and don't develop the skills and resourcefulness they need to truly be adults and navigate life.  A short term assist? for a very legit issue? perhaps.. but otherwise, it really isn't doing them the favor to allow them to live at a level that isn't sustainable for them long term.

Unless your inheritance is "more than you could ever spend plus your grandkids could ever spend" then at some point, the gravy train will have to stop and they will be middle age teens unable to know how to handle their own finances.

I agree with all of the above comments!!! 

I am actually a little worried for you that this is even a question. 

Of course you don't have to support your GIRLFRIEND'S ADULT CHILDREN from HER PREVIOUS RELATIONSHIPS. This is just crazy to me that it would be a question. Kick her out, seriously. I promise that her vagina is not magical and you can find someone much better for a partner in life. 

What you do with your money is 100% your choice. Not your GOLD DIGGING GF!!

no person in their right mind would think that their SO should support kids that are not theirs. The fact that your GF is brazen enough to not only think it but  is actually willing to say it out loud!? wow!! She really has a brass set 

She does not work and does not contribute to bills... what does she contribute!? Other than spend your money?

pack her crap and kick her out! Run as far and fast as you can from this narcissistic gold digger!

Sounds like a great time to do some emotional housekeeping in your life and interpersonal relationships.

What do you think would happen if you closed your pocketbook to all? Give some serious thought to that.

If you have to pay to keep people in your life, you need to give yourself a reality check.

my daughter is 20 and has 2 babies of her own and a fiance.  My daughter and my soon to be son-in-law are struggling financially so I pay most of their main bills, rent, utilities, phone, etc.  My girlfriend thinks that I should spend the same amount on her older children as well.  

Why are you financially supporting your daughter and her fiancé?  They have created a whole family with  not one but two babies and yet still expect you to pay most of their bills? How long have you been financially supporting them?  What's the plan for them to be financially independent?  All adult kids need to be working and supporting themselves including your daughter and her fiancé.

You should not be supporting your supposed adult DD-20 serial breeder non performing daughter or her baby daddy.  Period.  When they start breeding, the parental gravy train needs to come to a screaching halt. Your STB HS graduate DS-18 should have your support for college or trade school.  As long as he performs to accademic or training standards of his institution.  Once he fails to meed those standards, time for him to launch.

As for supporting your GF's children, there are a number of information elements to consider. Are they young?  Do they live in your home as minor children?  As a SParent you are not obligated to support your mate's kids.  However, you should ensure their health, care, and feeding when they are with you.

Beyond that, I would make any support of your mate and her children dependent on behavioral and performance standards that you set.  

IMHO of course.

Good luck.

Personally I spend whatever money I wish on my adult children. I do not ask permission from my husband and he does not ask what I give them. I consider it none of his business. I do not give any money to his children that is up to him.