After reading your updates OP, I think you would be wise to step back. Yes, children can become materialistic, but not only are the children coming to you when they want something, so is their Mum!!
In essence you are being used for what you can or might provide. The children aren't spending time with you because they want to, they're doing it, to see what they might get out of you. They've been quick to realise that you have deeper pockets than their Dad!!
You aren't responsible for providing material things for your step-children. That responsibility falls entirely to the children's parents. If their parents can't afford to purchase Nike swimsuits, then they don't have them, it's that simple. You aren't there to supplement their parents financial responsibility.
You equally aren't responsible for organising days out/activities for your step-children either. That should fall to their Dad, who should be doing this for his children. He isn't, instead he's leaving it to you, because it makes life easier for him.
Step back completely. Tell your husband that you will no longer be organising activities for his children and he needs to step up. They aren't visiting to see you, they want to spend time with him. Be straight with him...you are no longer funding his children either, because they see you as a cash cow.