Yes, it's absolutely appropriate to ask - it's going to affect your life and your choice to work there.
The right way to ask is straight up - "What's your work from home policy?"
That doesn't imply anything other than simply asking what the policy is. Don't apologize, don't justify - just ask.
Be prepared for a fairly well-rehearsed answer and hopefully a pointer to something documented formally. It's also OK to ask follow up questions - like:
- what equipment do you provide?
- do you require a certain degree of experience or demonstration of good performance?
- do you have requirements for the working at home employee?
Keep the wording open and judgement free. For example, "do you require a certain amount of time in the job or degree of experience before you allow work at home?" is fine, "what hoops do I have to jump through before you let me do this?" sounds like you think the hoops are unreasonable.
There's a point where at around 5 or more questions, it'll be pretty clear that you are REALLY interested in working at home and that any other option may be a no go with you. If that's true, then there's no harm in asking. If you would work there whether or not they have work at home, then ask a few questions, and see what you learn, but don't make this a 15 minute Q&A experience.
If you don't like the policy...
Depends on how far you want to push and what the market may be. If this is the 1 job opportunity you've had in the last 3 months and you know that you have a lot of competition, leave the critique to yourself if you want to work there. If you have tons of offers and it's hard to find people with your skill set, point out gaps that would be a real value add to you.
A job offer/acceptance goes both ways and has to be good for both parties. You don't want to take a job that doesn't work for your life - but they don't want to hire an employee who is such a special case, that it causes a problem with the overall pool of people working at the company.
Work at home has worked really well in some places and very badly in others. It's hard to know, across all industries and businesses whether you will be interviewing with a business that really likes it, or really hates it. If there has been a recently failed program, realize that now is not the time to create change.