Ted, I hope that the care package works out for you both - I had to arrange something similar for my mother earlier this year following a stroke and fall, although we had no free period from the NHS to tide us over, it was just pay from day one.
I would recommend that you carefully read the terms and conditions of any of organisation that you employ directly, for instance the first one that I arranged to care for mother charged one week at full rate and the second week at 50% of full rate for any cancellation of service through such events as hospital stays etc; whereas the second organisation charged only one day at full rate to suspend their services. With costs of around £1000 per week, the unused visits really add up!
The greatest problem that I had, however, was finding an organisation that would actually provide the package of four visits per day, few were interested in that level of commitment. In the end, the hospital discharge team put me in touch with a company in Crawley who, without charge, trawled through all of the available providers covering this area (central Norfolk) and then left it to me to choose between them (there were only three).
Unfortunately, it didn't work out for mother because she kept falling, and she is now in a local care home. Interestingly enough, the cost of that in one of their largest rooms (it is REALLY large) is less than the cost of four home visits per day from care providers. Aditionally, ANY overnight stay would have cost an additional £350.00 per seven - hour shift for home care.
Anyway, I do hope that it all works out for you both and although perhaps not too well yourself, you can find a way through it all.