It doesn't change your relationship, IME, what it does is massively change the dynamic. The problem with it is that the dynamic before DC is relatively easy, whereas after DC it will expose stuff that you didn't realise was a problem before - perhaps it wasn't a problem but the underlying attitude or whatever is always there. Conversely if your relationship is strong then it will highlight all of those great points about him and you'll fall in love with him even more, and he you.
You have to work as a team. Which means that you take an equal role in things like housework, bringing money in, making the house look nice, bills, cooking, etc. That doesn't mean necessarily that everybody does 50/50, they might be split up in other ways, or that it looks perfectly equal all of the time, but it means that your goal is each to make the other's life easier, and/or to get everything done without sniping over who does what, and respecting each other's contribution. Red flags for this are if he's lazy with the housework because he knows you'll pick up the slack, if one of you is doing far more than the other, if you don't expect the balance to shift according to variables like illness, tiredness from work, stress, preference, etc.
You need to support each other emotionally and mentally. So look at how you act when each of you is having a hard time. Are you (each) supporting, pushing, holding, uplifting even when you don't know what's wrong or are you criticising, questioning, ignoring, waiting for the storm to pass? Do you trust each other or do you tend to assume that if one of you is complaining about something that it's not as big a deal as they are making out?
Unfortunately this one is still gendered. As the woman if you take maternity leave and/or longer off work or return part time, your entire life will change in a way that his will not. It's impossible to explain how this makes you feel, so the support in the previous point is really key. It also puts you in a vulnerable position. That means that he has to be willing - really willing, happy, to support you. For red flags for this one you want to look at what he's like when you're ill or otherwise at your lowest points. Is he good and helpful and supportive or dismissive, perhaps even impatient?
One of the biggest dynamics it's going to change is money. It's likely that your earnings will dip, or his will, if he takes time off work. You'll have childcare to pay for if you both want to work before your youngest child is around 12 or 14 years old, which is likely. You REALLY need to have a proper "what's yours is mine" attitude to money and see it, and bills, especially family or child related expenses as joint. You can't really have "mine" and "yours" expenses. That means the stepson too - you're a family, there's no reason why that needs to come out of his personal finances. Of course it's fine to have separate pots of spending money as many people do this but don't end up in a situation where he's asking you to pay him back for things, or all of the children's expenses come out of your "pot" or you're splitting bills 50/50 when you're not earning 50/50, or he's expecting some kind of 1950s housewife deal "in return for his money".
You have to remember that you're not necessarily going to be the most important person in your partner's eyes any more. I'm sure if he has a DC already then you will already be aware of this so it's more the other way around. The DC will be the priority at times and rightly so. It can get extreme especially when they are little - you can feel touched out at the end of the day and just not be able to deal with another person needing/wanting you. You may feel pushed out by your partner. You (each) need to be able to put the hurt about that away and reach out and connect with them, not necessarily in the way you want, but in the way they want.
I am not at all suggesting that every man with DC from a previous relationship is an unsupportive father to the mother of their child, but it's a definite possibility which you can't really ignore TBH. You say that the relationship broke up because of stress over the child being ill. I know it's not nice to think about, but what if your child was ill, seriously ill? How do you think he would react in that kind of situation? You would need all of the support mentioned above and then some. You can't predict the future of course, but you can look at how he has acted in situations (with you or with his ex) in the past and see a pattern - people don't usually change their core, base reaction to situations. You could (and probably should) talk to him about it - it might be uncomfortable, but it might also be extremely important.
Good luck! I wish you all the best on your journey together.