First I'll say you're not doing anything wrong. Someone has to keep the house running. It's always a tough thing though, when one of both parties in the marriage are not running on all cylinders.
I don't know you guys personally, but from what I've read here it sounds like your husband is suffering from mild depression and could be functionally alcoholic.
I'm no chemical dependancy professional, but I am the survivor of a marriage that was once the exact scenario you described here. If my hunch is right, I think you're going to need to seek counseling and soon.
For us, we had to go to a marriage counselor to overcome this cycle of alcoholism. And it was a doozey because neither of us recognized this was the problem until we got into counseling.
This more common than many realize since everyone thinks chemical dependancy is when someone is knock-down drunk, DUI's and physically beating the stew out of someone. Another thing is people tend to think alcoholics are only those into serious mixed drinks and worse, while most think beer drinking is tantamount to having a diet coke. But studies show, most alcoholics are casual beer drinkers... not those high-ballers at the happy hour counter downtown.
Most alcoholics are what's called "functional." They are totally dependant on it, but it's just part of everyday life and very much under the radar because it's just a brewski or two after work or on the weekends.
It becomes alcoholism when it's a daily activity...even if it's only a couple a night. Dependancy isn't necessarily the amount so much as the "need" to have to have this in your life as part of your daily routine to function. Just like some people can't function without their AM coffee, there are people who can't function without their after work beer.
The warning signs are the lack of interest in anything other than activities that center around the beer. Depression is another tip off. Depression isn't always the person who lays around in their bathrobe in the fetal position all day. The inablility to connect with family on an emotional level is often the biggie. Lacking the will or even caring about the day to day activities necessary to live. Moodiness is a big part of this. They can be all over the map, and sometimes irrational. It's all about control.
You might want to look at your expenses and see how much he spends on beer and/or beer related activities. You might be surprised to see how much you spend. This can be another warning bell.
With us, my husband had two to three cans a night afterwork, and on weekends as many 6 or more while hanging with the guys, watching football, or working in the garage or yard. Over a day, it can get away from everyone how many are being consumed, so when you start checking the budget, sometimes it hits home then.
My husband had to go cold-turkey and hasn't had any alcohol for almost 5 years now. His whole behavior and attitude changed with it. He's like a totally different person. For him, he dealt with stress this way. He called it "relaxing" after work etc. so neither of us saw it as a problem.
But it really did get in the way. He waited for me to do everything, and became a bear when things didn't go his way. He called the shots from his arm chair, and all was right with the world when he had his beer.
If indeed he has a chemical dependancy issue, it sounds like in an odd way, "co-dependance" may have set in your relationship. You have taken on the world and have managed to keep crisis at bay. Unfortunately, this has facilitated his bad habits and perhaps hidden problem.
There is no way to tackle this on your own if you think this may be the problem. You need to get outside help. But you can start the ball rolling by telling him you feel overwhelmed by the unbalance in the situation, you fear in the long-run your financial well-being will be in jeopardy if he doesn't contribute more, and that in the years to come he may not have the relationship he wants with his daughter and you if he doesn't get more involved in your lives beyond t.v. and dinner time.
You both need to communicate with each other. He's turned to himself, beer, and tuning out in front of the tube as a way to cope with stress. And perhaps on some level, day to day life of really caring for a young child, and living up to your expectations among other more deep seeded things in his background are contributing to his depression and avoidance behavior. He needs to dump the crutches and you have to help him or you're both going to suffer in the longrun.
As for his not being so great at keeping the house clean, feeding your daughter, and showing her off at family events, this is common with many couples. I really think he loves his girl, and it's probably a real boost to show her off to his family. Don't take that from him. Especially since I think his bad Mr. Mom skills at home are more about something else going on with him. Also, most guys aren't raised to be Mr. Mom's. That comes with time. But can be a challenge when they have other outside issues getting in the way.
In the meantime, cut yourself some slack. If you need a get away, take one. All you're doing right now is heading for a big emotional and physical breakdown. You can't go at that pace with a young child for long.
Next, talk to your husband. Regardless of how he recieves what you have to say, be honest, patient and not expecting any resolution. This will only be the tip of the iceberg of a long journey.
Last, get professional help. And start with a good family counselor. Get books on the topic to help you know what type of questions to ask, and where to find resources in your area.
Don't expect him to be gunho to go see a counselor. The good news is he doesn't need to be there, for you to start the ball rolling toward getting help for all three of you. Many counselors will work with just one person of a couple and it can still benefit your situation.
Good luck and hang in there.