How give up the binky?

I wanted my daughter, who is 2 years old and cut her from her bink-bink (which she calls her binky) but I think I'm doing it at a wrong time, because my son is in the hospital with cancer and she is upset. But I want to get her off the binky before preschool because she sucks on her binky everyday even at nap and bed. I don't believe in lying like giving them to doctors or fire men because I taught my daughter that they save people and kids in need if they lost their mommies or daddies. I have actually tried tossing them in the trash, but she then found them when she knocked over her and all the trash came out. So that didn't go over so well so I had to wash them and give them back to her. I can't cut any of my children cold turkey. So what can I do about this? I also can't suggest giving them to her baby brother because he has his own. I was told with his condition that he might not live long, I can have her put her binkies in his casket? But I wasn't sure how that would go because she adores her baby brother. But what can I do to make her give up the binky in this stressful time or should I wait?