Oh Dave!
I wish I could give you a real hug instead of just a virtual one. You are at the sewer end of the pipework, and there's a load of toilets being flushed in your neck of the woods, right now.
I'm sorry that it's come to this, and that you haven't had your break. I can't understand your step-daughter agreeing to take your wife, when she must have known she'd be going into hospital.
Perhaps she realised how desperately tired you were, and though it wasn't the best time, may have been assured by her husband that he'd look after your wife, during her hospital treatment, and things got too much for him.
But, with regards to your decision as to whether or not your wife should go into a Care Home, I really wouldn't worry about anyone elses opinion, family or not. I know it's easy to say, but the bottom line is, you're the one at the sewer end of the pipework - not them. Only you, and you alone, know what the strain is like for you. It doesn't matter if you've been a carer for 5 months, 5 years or 15 years. If you're knackered, and, as you've posted on here, suicidal, what benefit is it going to be for your family, and your wife's family, if you're dissuaded against opting for a Care Home for your wife, but, as a result, bow out the picture. Permanently. Would they want that?
You're very brave and heroic to want to care for your wife for another night, but please don't put off seeking help in the morning Dave, will you. Else we'll all nag you!!