From the altered birth record, you probably know the father-in-law's date of birth and location. Likewise, I assume you know the date and location at which the adoption took place.
Those two dates and locations provide you with two points on a timeline. I would begin from the adoption date (and location) and inch my way back in time.
- What was the law and practice at the time covering this type of adoption. As for very general information, I reviewed the Wikipedia entry, "Closed Adoption," which includes the statement, "An adoption of an older child who already knows his or her biological parent(s) cannot be made closed or secret." For even more general information, see The Adoption History Project, "Adoption History in Brief."
Your understanding of the specific laws and practices in effect at the time the adoption was undertaken should guide the steps you follow to learn the details of the adoption. You would presumably seek any court records or documents that you or your spouse may be entitled to receive. - Marriage of grandmother to her second husband. It isn't clear to me from the question whether you have the name of this husband, but if you have her death record/cemetery record, etc., then you should be able to learn that name. The marriage record would report the grandmothers name at the time of the marriage--that might be her married or maiden name. (Marriages and/or marriage licenses are sometimes announced in a local paper.)
- Divorce of the presumed biological parents. Assuming this divorce occurred when/where divorces were documented/recorded, you should seek these records. You will need to learn where the divorce was entered; start with the locations where grandmother would have lived, work toward the location where her son was born. Continue to broaden the search until the record is located. (Divorces are frequently published in local papers.)
- Intervening census. Lorraine mentioned that depending on the time of all these events, there may be a census record or two in which you will find the grandmother either with her son or with former husband, or both. Depending on how size of the town and the names, you may even be able to location prospects for this by doing some creative census searching.
- Marriage record of later divorced parents. Even if you do find a record of the divorce, I recommend you find this marriage record. I would do it anyway, but would hope to learn if that marriage happened before or after the birth of the son (your late father in law).
Note: You did not mention whether the son (your late father in law) had any siblings, but if there was more than one child born to the divorcing parents, there may be even more records you could seek.
Ah ... I see there is an intervening edit to your question. I may edit this post after reviewing your changes.