The chances of rehoming a feral-type cat with major health issues is virtually nil. Conclusion: either you take on the responsibility for this poor cat, leave him to his fate, or pts.
I would take him on. As to the prognosis and long term costs, only a trusted vet can tell you this. He will probably lose his eye if the biopsy is bad news, but that may be better than losing his life. Ask your vet if he could tell during the op whether the chances are that this is cancer, and if he thinks it is, to remove the eye there and then. This will save the trauma and expense of a second op.
Do you have a spare room you can keep him in during recovery, where he won't come into contact with your own cat? If so, keep him in it for a couple of weeks while he recovers from the op, during which time you could build him a small kennel-type affair in your garden.
When he's recovered, let him out, feed him in or near his "kennel" and allow him to live out the rest of his days as a garden cat.
Do you have a cat flap? If so, it may be best to keep it shut or get an electronic one so only your cat can come in. This will give your cat a safe bolt hole.
The initial costs of this will be high (by the way I think your vet is expensive) but your children would be upset if you took any other action. Have a chat with vet and hubby, see what they think.
