He says he won't decrease the days he has his daughter, but he is not providing the daily care for her - you are!  That is not YOUR responsibility, it is his and BMs.  The fact he isn't listening to you about the issue is a red flag.  IMO it shows he does not care about your life and happiness, as long as his daughter is being cared for.  Not a good foundation for a strong  marriage.

I would ask him the following hypothetical question:  "If something were to happen to me, what are your plans for taking care of the children?"  I'd be interested to know what his answer was - especially for his daughter.

You are in a tough situation since it appears you cannot currently afford to leave if you had to.  Is there a possibility that you can go (with your son) and visit some family or friends for awhile?  Even it it's only for a week or so, maybe it would be enough that your DH would come to understand how much you do for HIS daughter.

Aside from that, be prepared that this situation will probably worsen the older that SD gets.  She will undoubtedly continue to have "issues" because of her mother's disinterest in her.  This will manifest in increasing hostility to you, since you are NOT her mother but are stuck in that role.  SD will use you as the whipping post for her anger about her mother.  You've got a long way to go before she ages out.  Her presence in your household will continue to have a major impact on your relationships and your finances, so you must acknowledge that fact.  Learn to live with it since it appears your husband has turned a deaf ear to your pleas for understanding.  

Wish I could offer you better advice.  Ultimately, though, you must FIRST take care of you and your son.  Whatever course that may take. 

Just a minute ... if she's at your home a majority of the time, why is her school so far away? And does your dh REALLY expect you to be on the road for THREE hours per day when she's with you?! That's enough to make anyone feel resentful.

As for him not wanting to reduce "his" time with her, well, that would be fine if he were actually with her. But he's not.

Ask your dh how he's going to cope with her when you decide to go back to work (I'm assuming you don't have a job because he ' expects you to be able to take care of your SD at the drop of a hat).

I understand you love, i understand your resentment and why you felt the need to ask DH to reduce the time because SD's presence is inconveniencing you and giving you extra work and not DH. You probably don't enjoy having to take responsibility that's not rightfully yours. That's enough to get you resentful. It is your husband who is the problem because he is expecting too much from you and its unfair, he shouldnt be okay with giving you so much work and inconvenineces that should be his. What would he do if you were not there? Let him hire a maid to do all those things for his child and give you a break. The biological parents are honestly the reason why step parents end up resenting their children. It is the way they position them in our minds we start seeing the step child as an extra load, burden, and inconvenience and tha'ts enough to resent them because they are not our relatives to begin with, we owe them no favours and have no obligations towards them. If your boss started giving you tasks that are not on your job description wouldn't you get mad and resentful? Won't you feel used and taken advantage of? Probably your DH is not taking into consideration that he is making you resentful by burdening you with his responsibilities. I suggest you talk to a consellor who will make him understand all that. If DH did everything for his child and didnt bother you or if he found a maid to do it for him i don't think you would feel resentment towards the child?

I too ended up hating the existence of my step child yet it was not his fault but his parents by making SS my problem and his lack of parenting. I understand your frustration and resentment. Feel free to inbox me if you want to vent to someone who totally understands and won't judge.

Im a soon to be step parent and understand your frustrations to the point of rethinking the whole relationship. This is exaclty why blended famlilies do not work. Once you have your own kids you become resentful towards the skids. Although it is not the skids fault for feeling the way she does her behavior in unacceptable and should be addressed. Your husband sounds like a lax parent who expects you to pick up all the slack for this mess him and his ex have created. Ultimately your husband is to blame here, not the skid. Remember that. What would he be doing if you weren't around? He needs to hire a sitter for his skid or drop her at bio moms, grandmas place for awhile, so you can parent and give you a break.  hugs!

If you are fantasising about flats then it is time to get some marriage counselling NOW. Counselling is a lot less expensive and time consuming than a divorce. You know that if you did divorce, given his track record, he'd want a lot of time with your child and he'd be dumping him on some other resentful woman. 

Resentment is a killer and I'm not saying that you don't have every right to feel that way, but it's no way to live. I've been in a resentful, point-scoring marriage. Now, I'm with someone who loves to give and I feel gratitude every day. He is away this weekend with his kids and I miss them all.

Don't let another minute pass before you start investigating counselling options. You are angry with your husband both for dumping his kid on you and for not stepping up to the plate enough with your shared child. But it's easier to focus resentment on a child who has no blame in this at all. If there was no home where you were 100% wanted you'd feel that way you might be whiny and needy, too. As much as you resent resources going on her, she could equally resent resources going on your child. 

I could focus a lot of resentment on the fact that my partner is on his ex-wife's mortgage meaning we're having housing problems (actually I do a bit). I could focus on the fact that a lot of money goes out of his pay packet each month to her, but I'd still love him if his salary was the net after child support - that's just the money he has available.