Thank you for asking this important question and for caring about your mother-in-law's peace of mind. You're not alone in wondering if cremated remains are mixed with other remains. You
are exactly right that he would be cremated alone. It is against the law to cremate more than one person in a cremation chamber (known as a retort). It is therefore, only that person's remains that would be put into the urn or container. The remains she gets back will indeed be his.
Keep in mind, though, that no matter how diligent a crematory operator is, there may be minute particles that remain in the chamber and it is possible that they could be removed with the next person's remains. This is an extremely small, miniscule amount. It might help to think of it this way "“ let's say that you drop a five pound bag of sugar on the floor. You very carefully sweep it up, trying to get every single bit, and put it into a container. A few minutes later, I walk in with a five pound of sugar and I also drop mine on the floor in the same spot. Now I sweep mine up and put it into a container. Is it possible that there were a few very tiny granules of sugar from yours still on the floor that got swept up with mine? Yes, no matter how careful you are, it's still possible, but you can see that the amount is very small, almost microscopic, compared to the entire container.
Even though it's a small amount, there's still a section about this on almost every funeral home or crematory's authorization form that reads something like this -
"I understand and acknowledge, that even with the exercise of reasonable care and use of the crematory's best efforts, it is not possible to recover all particles of the cremated remains of the Deceased, and that some particles may inadvertently become commingled with particles of other cremated remains remaining in the cremation chamber and/or other devices utilized to gather and process the cremated remains."
One thing that may be helpful is for you to call a local funeral director, express your concerns and ask if he/she could make arrangements for you and your mother-in-law to visit the crematory. When you do, the crematory operator will answer your questions, talk about their procedures and show you whatever your mother-in-law needs to have peace of mind about the process.