You aren’t married and so I can understand separate finances where there are disparate incomes and he has a child from a previous relationship- even now that they have joint children. It would not be what everyone would want or choose, but I can understand the logic behind it. Ultimately, OP chose to stay in the relationship when she knew her partner did not want to get married and did not want to share finances and then chose to have children with him. OP- did he promise marriage or shared finances? If he did, and changed the goalposts, then that is a totally different situation than if he was always clear he had no intention of getting married etc. If the latter is the case, I don’t think you can be too annoyed that he has stuck to that- if it is the former, he has behaved unfairly (though as you chose to carry on the relationship despite this, it’s not all on him).
I understand why you might not like the set up, but it is not as though this has been done to you against your will and you had no say at all. If you aren’t happy now, you need to decide if it is a deal breaker and you need changes to happen or you will end the relationship. If it is, then communicate this to him. If it is not, then you can still speak to him about your frustrations, of course.
Regardless, I think he should be doing essential maintenance of the house without quibbling, it’s actually counter-productive not to- but I think it is ok to spread non-essentials out over time rather than as soon as you notice them/decide you’d like x done. He might be resentful as he feels as though OP is keen to spend money on all sorts of things- loft conversion, new porch, new decking, a holiday etc- but doesn’t have to contribute to the costs of those things. It’s easy to say “it’s only £x” when you don’t have to provide the money for it. I don’t know how much your mortgage and bills are- but if substantial, perhaps he doesn’t have masses of “spending money’ himself after all the bills etc (i’m not saying he has none, as he clearly does, but perhaps it is not as much as OP thinks it might be). Of course, if he were more transparent with his finances, it would help OP understand, so that is partly on him.
I suspect he feels he pays quite enough in days to day costs and possibly wants to prioritise other things such as pension or savings over things he sees a less important (e.g. a holiday or new decking). whereas you are prioritising spending now in order to have nicer things and experiences- I would not say either of you are wrong, but it is clear your priorities are different. He might just be quite careful with money, or perhaps he is just a bit tight fisted- I can’t be sure, really. Or he might think that he pays a reasonable proportion of the costs, and if you want to spend more on holidays and non-essentials, that it is up to you to provide the money for it? I accept you can’t work longer hours- I would imagine he does too, but perhaps he thinks that this being the case, that means that you can’t do all the things you would like.
I suspect the tenants in common on the mortgage is to protect his older child’s share of inheritance in the event of his death, rather than solely to screw OP over.
I would strongly suggest you do have a discussion re life insurance, Power of attorney, wills, who is named on his pensions as benefactor in case of death etc- it’s important these things are in place/you know what is happening, just in case the worst should happen.
in relation to your individual finances- you have £1200 in income. I assume as you say he pays “all bills” and your money is “treat money”, that you mean he is paying utilities, council tax, insurance, groceries/food/cleaning products and buying household equipment (e.g. washing machine, freezer, cooker) if they need replacing? If so, the only expense that you are committed to is the cost of running you car, paying into your pension (is that through your employer?), paying off the credit card and your children’s hobbies/clubs. I would think that should be manageable on £1200/month.
Is the car on finance or just running costs? If latter, unless you are doing a lot of miles, spending a lot on maintenance or have high insurance costs (e.g. points on your license) then you probably aren’t spending more than a few hundred per month on it. Not sure re your pension, of course, but if you are only earning £1200/month I would not have thought your contributions would be particularly high unless you are paying voluntary additions. So you must have a reasonable amount to spend on treats/DC clubs, i would have thought? Are you paying for his DC too or just the twins? They must either be doing expensive hobbies/sports or quite a few clubs each to be spending hundreds of pounds per month. Perhaps you need to review this- if your DP objects to cutting things back, then I think you have to suggest he pays for it as you cannot afford it.
Given your DP is paying the mortgage costs, all bills, maintenance and home improvement costs, I don’t think i could begrudge him buying himself one expensive piece of equipment, unless bigger ticket spending on himself was something he did regularly to the detriment of other essentials and things that would benefit his family- in which case I think it’s a different story. But, as a once off, which does not impact on anything else? I think it is absolutely fine.
I think the holiday on OP’s credit card is a red herring. He did not feel it was necessary and so did not agree to finance it. Op decided to book the holiday and pay for it anyway, without asking him. And because she decided to do this by herself, and pay for it herself, she was absolutely within her rights to do so. What would not be fair is to then expect him to pay for something she decided to do unilaterally. It’s not like a holiday is an essential or something everyone prioritises. We don’t go on abroad holidays every year, even though theoretically we could afford to- a few reasons for that, not all financial considerations. My point is, they aren’t a big thing for everyone, so if OP was adamant that they needed to go on holiday and he did not agree, it’s fine for OP to finance it in order to get what she wants- and to do so in any way she choses- but it is Nobody forced her to book a holiday, nor to put it in a credit card, it was a choice she made. Even if borne out of frustration of not being able to persuade him to take a family holiday- which is a perfectly reasonable thing to want to do, I agree- but her decision nonetheless.