big hugs. this is not the first time on mumsnet i have wanted to come and give some one a big cuddle. I feel for you, when you said about not knowing if your standing up for yourself over the wrong things and being lost in whats right or wrong. It's a struggle when you are so deep in to be able to see anythign clearly.
First things first you need to be thinking as clearly as possible and be calm. I don't know if your kids are school age and what time you have in the day, but go out to the park where ever, out of your house and all the built up tensions. Work through the things that your angry about, let yourself be angry, the kids aren't watching, your not going to offend him, sod reasonable be angry till your tired of being angry.
At this point your probably feeling somewhat empty so start to think about the good things, about yourself, your partner and your kids (This can be hard when your depressed but one each will do.) Smile force it if necessary just to remind your face what it feels like! Think about your kids acheivements, their first giggles.
This may sound silly but it's important to break the behaivour pattern of depression so you can start to operate on a happier level.
Pick one or two things that are the most important things, you think you / he can realistically change.
Go home, smile at him, do something nice together, whatever you both enjoy.
Pick a time and place to talk to him that is non confrontaional, tell him that he is making you unhappy, tell him what and why, ask him to suggest resoultions that he feels work for him and that he can realistically stick to.
When someone is mentally ill it is sometimes necessary to make allowances for their behaviour. Do not take this to mean that he can always use that as an excuse to get out of anything he does not feel like doing. We all find things a bit much sometimes but it doesn't get better if you hide away sometimes you have to make your self face the world. It is incredibly difficult to be certain when to give someone the little push they may need and when to help them hide, you will have to make that decision for yourself each time. I would say that hiding should not be permanent. Ok if he needs out of a situation to calm down and get his bearing but after that he has to come back and carry n not just stay away.
In deciding when to stand up for yourself here is something I learned from consenus decision making, do not block a consensus decision of the group unless you are willing to leave the group over the issue.
So is the issue you are thinking of raising with him so important that if not resolved you would no longer wish to continue the relationship. If so you had bloody well better sort it out come hell or high water, if not maybe you can work round it.
With regards to the refusal to make plans, this is what i do. Make plans anyway. Tell him about them, where possible leave the option open for him to come or otherwise, let him know when he has to decide by and leave him to it if he misses out thats his worse luck. You will probably find that he ends up coming along and enjoying it but don't let it stop you if he doesn't
Step kids are a difficult area that I don't have much experience of but i would like to say that kids cooped up in the house (especially a house they don't neccesarily feel 100% at home in) are likely to misbehave. Step kids are more likely to boundary test you. Arrange to take them out with or without your partner. Do it at the begining of the weekend so that you have apositive experience shared to start the weekend with and you are not tempted to take it away for bad behaviour (or resent doing it after bad behaviour) Try to have something that you go out and do each weekend, from what you say money is tight, there will be free thhings in your area, Istrongly reccommend a local country park or nature reserve (a bit of space for them to run off steam) It's summer there are lots of berries and things growing, look up what is in season and take them to get some.
this has already been quite long so i shall keep these last points very short.
Don't carry on about him giving up smoking,( i smoked for 11 years, i stopped a year and a half ago)it won't make him quit, it will just make him want a cigarette!
Sometimes it's ok to lose structure and sanity, if you have it most of the time your doing well!
This may or may not be the best advice for you but i feel obliged to include it. Many weekend dads don't seem to bother with the kids when they come for the weekend. I can't understand it personally but i do know the only way they will notice that something needs done is if you stop doing it!!!!! You will almost certainly be unable to do this when you are there so don't be. Get a weekend away, stay with a friend, your mother, someone. Let him realise how much you do by not doing it. plus a bit of missing each other never did a relationship any harm!
Most importantly, make a little bit of time for your self, the rest of the world will still spin, you may have to pick up the peices later but it will be worth it. Lock yourself in the bathroom if neccessary, just find ten minutes in the day to call your own. Paint your nails, apply moisturiser, read a book, massage your face (no really, try it!) do something that makes you feel good.