Does your brother-in-law seem to live in a half-million dollar house? Does he have a job that would allow him to do that, and does he drive new cars?
Since your MIL went into a nursing home, what are the arrangements? Is medicare paying for her care?
I wouldn't say no outright to helping them, but first I'd have a family meeting, and I'd insist on knowing details: who's paying for the nursing home, what is the bankruptcy status, look at the dental exam and the dentist's recommendation, what health insurance do they have? What financial shape are your in-laws in, such as bills owed, bills being paid on time, savings, health insurance, etc.
Unless your FIL is completely transparent, then you don't help. If he is willing to share everything and he's bankrupt but buying cars and houses and not providing for your MIL's care, then you don't help.
No details, no information, no help. If he won't allow you to talk with the nursing home with him present, or if he won't allow you to be present when he asks the dentist's office about the planned procedure, then no help should be offered.
If you ask someone for money, you should be willing to be up front about exactly what the needs are and what the resources are. Maybe that will give your husband some peace of mind: your're not saying no, you're just saying you need information to make an informed decision about such a large amount of money, and to make sure the money is being well-spent.