From what I understand, the idea of a 50/50 split is related to divorce settlements, not care home fees.
I don't think you will be able to claim that your wife has no income and expect not to be charged, unfortunately. If her name is on the deeds of the house, it will count as an asset in her name, so fees will be charged against that, as well as any savings, although the house will not have to be sold as long as you are living in it.
You might need independent advice, but it looks as though what you are hoping to do (if I have read your post correctly) will count as deprivation of assets, which will be picked up very quickly.