Interesting question. "Problem" can collocate with both "with" or "of." Examples: 1. The problem with Sally is she talks too much. The problem with the car is that is has a flat tire. He's having a problem with his best friend. He's having a problem with math. Use "problem with" when (i) you are talking about a person or thing that suffers from some defect or problem, like Sally who talks to much or the car with a flat tire, or (ii) you are talking about a person having a difficulty in a relationship or in accomplishing something, like a problem with a friend or with math. 2. The problem of overpopulation led to China's 1-child policy. The problem of global warming cannot be easily solved. Use "of" when you are talking about a bad thing causes problems for you or other people. I hope this helps.

Only 'with' is natural. I don't think any of them is idiomatic. I think 'problem' always collocates with 'with' before a situation of some sort.

I would say "What's the problem with deciding on a holiday?" I might specify what you are deciding. Are the example questions rhetorical questions? For example, "What is the problem with deciding where to go on holiday?" I don't think I have ever heard that question asked. Americans tend to say vacation when talking about a break from work or school. British tend to say holiday instead.