Is she obligated to pay anyone else from the profits accumulated from her deceased mother’s music?

The mother of the deceased man should consult with a good lawyer who knows about wills, trusts and estates. The man's music recordings and the underlying intellectual property, which are the song music and lyrics, are both considered valuable property that did or should have gone to someone in his will, if he had one, or in his estate. The lawyer who handled those things at the time could best help you. The mother should also speak with a music lawyer who works with small independent musicians and record labels, such as me. It would be important to register copyright on the songs and on the existing recordings, if they have not already been registered. A copyright search would be done. The man created those things, so he owned the copyright, and copyright usually passes to the family. The law in this situation will be a combination of estate law, to see if he left these things to anyone in particular, or if they have generally passed to heirs, and to copyright law. It is important to see first who has control over the materials is it the mother, the mother and children, the children or someone else altogether? One thing to consider is that unless the man was already quite famous and his work is already well-known, there is not likely to be any profit from his music. Most likely, this will become an important family memento, but not be a moneymaker. But if the man and his music were already well-known, the music released after death could be quite successful.

If your friend died without a will, it is possible that his children own the copyright to his music. If he had a will, the music belongs to the beneficiary(s). Your friend's mother first needs to find out if she has the right to distribute the music. If she doesn't, she will need to license the rights from whoever does own the copyright. If the children are minors, their mother will have the right to act on their behalf.

When someone dies, the rights to intellectual property are similar to the rights to physical things somebody gets the rights. Was there a will? What happened in probate? Was there a trust? You can absolutely start a record label, record the music and sell it, and publish the musical composition for sale for any music to which you have the rights! You need to go back through the will and any probate court order. You may need to take all that to an attorney who specializes in wills. If the estate had an executor, that person might be able to tell you who has the rights. If the mother doesn't have the rights, the mother could certainly sign a contract with the children (if they have the rights) to publish the music. Since your question reveals fairly complicated issues under the surface, you should consult with an attorney for legal advice. The power of attorney may also come into play depending on what it is for, specifically. Again, this situation is complex enough that you need an official consult with an attorney.

This is a bit too complicated to give a general answer to, since there is relevant info missing from your question. Your friend's mother should consult with her attorney about this.