Leave him.

You need a partner, and he truly is just another child. Seriously, he is a FATHER and he can't keep a job to take care of his own kid?

If you want kids and marriage, find someone who will help make that dream a reality. He is still mopey because BM left him, and he will never be hapoy with anyone else so long as he pines for her.

I'm sorry that your heart wants this man, but there is no future with him.

Why is it okay with you to live with an addict?  No good will come of this unless he gets some help. There are support groups for people addicted to computer games.  So far none for family members akin to Al-Anon but there's always Codependents Anonymous.   You might want to check them out. 

And why is your mom putting up with this too??

I agree with the other posters, he is using you and still in love with BM, stop allowing this!  You deserve better.  Who cares if he can't afford it on his own....that isn't your problem...you are enabling him to sit around and play games all day while you do all the work for him.  His daughter is not your responsibilty.  Please, please do not allow this to continue.  It will only get worse for you!  

Forget about the BM. This has nothing to do with her.

Focus on you and your SO when you think about this.

Don't make this about your insecurities, your jealousy of his ex, or where he will go if you break it off. Forget all that. None of it is at the root of your problem.

You already know you want something out of life that he doesn't. So why continue?

Look at just the facts:

You want kids and marriage and he doesn't. That's it.

You have a goal to have children and there's an expiration date on that for women. You have a goal to get married and there is a "sell by" date on that for women. You don't have time to waste on him. If you wait too long to dump him, you'll be stuck, again, because at a certain age, all that's left out there for women is broken men from broken relationships and their broken offspring.

Resolve to end the relationship. Then figure out the logistics of getting him out.

Talk privately with your mother. Come up with a strategy to move him out. She can take the burden off you by playing the bad guy and saying she is tired of the living situation so he must go. She could say she wants rent from now that you can't afford on your salary. She can say she's selling the house, but first she needs to move out the slugs, so he must go. Plans change, so after he's out, your mom changes her mind about selling. Say what you must to move him on.

Or you could simply lay down the law with him, demand he get a job by a certain date, demand he tend to his own kid, demand he get his shit together, and if not, he must go. I don't recommend this because you might lose your resolve and waste more time with him. You want to be happy today, right? So you must start working on it today.

Or you could simply tell him you're two people who want different things out of life and you don't want to compromise. If you want him out with less of a fight, just put it to him that way and don't give him time to shape up.

If all else fails, get your own place and then break it off with him. You can always move back to your mom's later, but it might be easier to get him out when you're also going.

I understand you'll feel awful putting him out. But imagine how awful you'll feel when you're 55 and he's still playing videogames in your mother's basement and you're still cleaning up after HIS kid.

There's a reason his ex left him. She was smart. She probably saw he was full of promises he could never meet. You have to be smart too and do something that's going to be uncomfortable and messy, but you'll be glad you did. As it is now, you are going nowhere. At least without him, there's hope you'll make the life you want, but you must clean up this mess you made first.

Do NOT allow any more men to move in with you ever. When you find your prince, marry him. Shacking up is just a messy way to lock yourself into a dating relationship that has all the crap of marriage but without benefits. If he's not good enough to marry, don't shack up with him...but I probably don't have to tell you that now.

If you have any suspicion he could be vindictive or violent when you turn him loose, come back to StepTalk for more advice. In the meantime, go find your happiness. Get to work on a plan. It might take longer than you think to get him out of your head and your mom's house, so best you start today.

I am not usually one to say leave, but in this case, my only advice to you is LEAVE THIS MAN!!!!!!

He makes you feel insecure.  He will not give you what you want (marriage, babies and just being a decent adult partner).  He is not working, and is sponging off you and your mom.  He's treating you like a maid and a babysitter.  You may love him (or think you do), but he is not showing by his actions that he loves you, at all.  I hate to be so blunt, but it seems like he is just using you.  Don't worry about what will happen to him if you throw him out.  That's his problem.  At this point you're just enabling him, while destroying your own self esteem, and that's not doing him or his daughter any long-term favors.  He'll figure it out.  He managed in the past, and he can manage now.  Take care of yourself, and get this user out of your life.

I agree with what the other posters said, and also - your poor mom! Give her a break! It's bad enough she still has to support you, you also impose on her your slacker BF and his kid? That's insane!

Nothing about this guys says, "Keeper". Lose him.

Ask yourself what you are getting out of this relatioship. From what you wrote it appears to be nothing. If you want marriage and kids and he doesn't, he's not the guy for you. Please don't think you can change him. Don't wait around for that to happen, you will most certainly regret wasting your time. 

my jealousy and insecurities

You are not jealous or insecure. He is gaslighting you.

You want a partner who works. He doesn't. He's a game addict.

You want your future children's father to be an involved dad. He isn't.

You want a partner who pulls his own weight. He doesn't.

It's time to pull the plug on this relationship. Get your mom on board with you and get him out of the house. Since its mom's house she may have to go the legal eviction route.

Your sweet, kind soul is being used, abused, and trampled. You need a real man, not this parasitic noodle. I know you love him, but he's not a partner, friend, or good father to dump his kid on you.

You're good enough to be free from this not-gonna-get-better nightmare. Run.

I was going to suggest that you have a come to Jesus meeting with him and tell him exactly what you need out of the relationship -- job, marriage, children.

But you know what? Forget it. He's already shown you that he doesn't care about you. I rarely tell posters to leave the relationship, but will make an exception for you. There is nothing to salvage here.

You're in love with who you think he SHOULD be, or some fantasy based on who he has been in the past. But he can't sustain the good part of who he is. You'll end up old and bitter and broke and childless if you stay with him. You deserve much, much better.