Kakey, I am also married to a widower and stepmum to his two (teenage) kids.
My DSCs do have issues arising from the loss of their mum, of course they do. They also have learned how to fall back on the loss of their mother as a strategy for getting what they want. Both things are true. Sure, people are going to tell you that you are heartless for noticing that, but it happens. Children of divorced parents do it too. It is pretty simple, really - kids notice if something works. What I have tried to do consistently with my DSCs is to accept their feelings, but not their behaviours. Kids also need to understand that many people have hardship in their lives, and terrible losses, but that they can use this to develop their empathy and kindness towards others.
Children who have experienced a bereavement need clear boundaries and limits, as much as other children do. It doesn't do them any favours to allow them to define themselves, or be defined by others, by their loss alone. I think it is probably also important that the roles in the household are clearly defined - my stepkids needed to know exactly what role I was going to play in their life. DH and I could honestly have done better at communicating that from the beginning, and establishing just how much of a "parent" I would be. I don't think there is necessarily a right answer to that, but I do think it needs to be made clear to the kids. (Like exotic says, maybe the answer in your family is that you will play an equal parenting role to the kids. In my case, the kids were older, and my role therefore was different - and a bit different with each kid, actually - so I am more involved in the 'parenting' of my DSS than of my DSD - because of their ages, needs, and temperaments, and the chemistry that we have between us.)
We had some behavioural problems with DSS last winter. In the end (and it was rocky getting there), DH and I agreed that we needed to address both aspects of his behaviour - the emotions behind his actions, and his actions. He'd refused grief counseling after his mum's death, and DH and the counselors said there was no point in pressuring him to go if he didn't want to - but after he started acting up, and justifying it to us by bringing up his mum's death as a principal cause - then we told him that we expected him to talk to a counselor. He went for a half-dozen sessions and no more, but I think it did help, and I feel that now he would be more likely to go again if he feels he needs it. We also gave him consequences for the rules he had broken.
If you want to talk about this, you can always message me. I know what you are up against.