Assuming that you are going to do as stated, and loan the money despite the many good reasons against, my advice on the best way to do it is to set milestones, and loan based on that.
For example, we will loan you:
$5k immediately (assume this is a gift)
$5k after you've developed a sustainable budget (...that has no more luxuries than your budget)
$5k after you've met with a financial planner or bankruptcy lawyer
$5k after you've put your house on the market
$5k after you've accepted an offer on your house
$5k after you've been able to keep the balance on the credit card lower/same for 3 months
If they can't meet targets you* establish, you KNOW you are throwing away money with the credit cards as the only winners. You also have an easier way to stop the bleeding, if they fail to do any work themselves to fix matters. This follows the "never help someone more than they help themselves" maxim.
[ETA: *To clarify, you here can be a joint you, I'm not saying this needs to be a unilateral command. If you can get them to sit down at the table with you and figure out next steps, they'll have some ownership over the steps and are more likely to want to make them happen.]
Privately, see if you can get your spouse to agree - in writing - with you for next steps. e.g. if they complete all of the steps, we'll forgive the first $5k afterwards. On the other hand, if they do not do a step, they don't get the milestone money. If X, then we won't give anything more other than help with a bankruptcy lawyer. (It's pretty troubling the spouse refuses to even acknowledge the looming possibility of bankruptcy. My guess is the relatives are even worse on this point.) As part of the conversation, consider making explicit and immediate the tradeoffs of loaning the money (e.g. together agree that you will take a camping vacation instead of a trip this year to save some of the $30k, that you will cut the dining out budget by 50%, both work overtime, etc.) It's dramatic, but you might also consider a postnup agreement regarding loaning the money.
[btw, everyone keeps talking about it being the wife wanting to loan the money. Did the OP ever say wife? I thought the OP kept it gender neutral. Just an interesting observation on MMM crowd assumptions.]