My wife said something to me last night that raised my eyebrow. She said when Jesus died (was crucified), that he came back to life (in the flesh) and walked the earth for 81 days. I know that when Jesus died, his soul arose from the dead. But not in the flesh.  Which is right?

I have to give your wife the nod on this one--with one correction.

Jesus did appear in the flesh after his resurrection. In Luke 24:39Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
See All..., He told His disciples when He appeared to them after His resurrection, "Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have." He specifically states that He was made of flesh and bones and not just a spirit. In another post-resurrection appearance, Jesus ate bread and fish with the disciples (John 21:12-13 [12] Jesus saith unto them, Come and dine. And none of the disciples durst ask him, Who art thou? knowing that it was the Lord. [13] Jesus then cometh, and taketh bread, and giveth them, and fish likewise.
See All...). These were not the actions of a spirit.

However, we need to remember that this body was a resurrected body--like the body we will have when we are resurrected. This body is also called a glorified body. The glorified body does not have the limitations of our present body. Jesus appeared in rooms where the doors had been shut and certainly locked: "Then the same day at evening, being the first day of the week, when the doors were shut where the disciples were assembled for fear of the Jews, came Jesus and stood in the midst, and saith unto them, Peace be unto you" (John 20:19Then the same day at evening, being the first day of the week, when the doors were shut where the disciples were assembled for fear of the Jews, came Jesus and stood in the midst, and saith unto them, Peace be unto you.
See All...). Christ never passed through closed doors during His earthly ministry; only after His resurrection.

1 Corinthians 15:44It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
See All... speaks of our death and resurrection: "It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body. " The spiritual body is what I earlier called the glorified body. It is the body of the saints when it has been resurrected. It is an incorrupt body, but it is a body.

Now, the one correction. The amount of time Jesus spent on earth after His resurrection and before His ascension into heaven was 40 days. Of this time, Acts 1:3To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God:
See All... states, "To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God." We are clearly told that He appeared for forty days on earth. Also, He ascended before the feast of Pentecost which occurred exactly fifty days after the feast of firstfruits, a feast that coincided with His resurrection. That means that the believers prayed for ten days before the day of Pentecost for the coming of the promise of the Father.