What exactly are you trying to teach your children? Are you trying to teach the children how to manage money? Are you trying to teach them about responsibility? Or are you trying to teach them that life should always be "fair and equitable?" Life is never fair or equitable and anyone that searches for that to be true ends up very disappointed. Instead, we can focus on teaching our children how to deal with how life is and give them tools to resource themselves when life doesn't turn out the way they think it should.
Too often in blended families we lose sight of what is the real issue. We often get caught up in making sure everyone is "happy" rather than making sure that each person learns how to feel their feelings appropriately, how to have open,clear, and direct communication, how to problem solve, and how to move through a crisis, disappointment or loss.
Sometimes, as parents, we try and make sure that our children never face "bad" or "hurtful" things. In reality, you are taking away their chance to learn tools that will help them when they get out in the world and have to face life head on. Rescuing our children from feeling negative emotions or from facing tough/painful consequences does not help them. It only robs them of the gifts and lessons they could and need to learn in life. Instead, support them in working through their "negative" experiences. Fixing or changing how they feel is not the goal. Allowing them the space and giving them the tools to feel their feelings and experience the consequences supports them in maturing.
As far as tying money to chores or not. Again, what is the intent? If you want to teach them about managing money then however you provide that money isn't the issue. If you are trying to teach them about responsibility then the experiences need to be directly linked to -- here is the responsibility and here is the consequence and then be consistent.
Often, when we take the time to really define what the actual purpose to our rules is it becomes much easier to define the rules and consequences. Sometimes though it is a little tricky and we have to be willing to be totally honest with ourselves, as parents, about what our real motivation and agendas are when it comes to our children. We have to be careful that we aren't setting things up for our children with the hidden agenda that it is simply to make our life easier or to not trigger our own unresolved issues.