What SHOULD happen now is that the metadata of MC are 'pushed' to all mp3's. In this case the lyrics of the song I changed on computer A.
This is what happens, though: MC reads the tag info of the mp3 and 'pushes' that into the database.
"What YOU WOULD LIKE TO happen" is what you should say.
Restored data is not pushed automatically between separate libraries, so if you have sync configured to run in the background it will overwrite the changes. If you edit tags on PC-B however and if you have the lyrics tag set to write to file it will "push" it to the file. (not recommended you want one master library and one master set of Mp3s I would think)
After restore you would need to run in library tools "Update Tags from Library" (right click after selecting files) on PC-B.
hope you can help me with a solution!
Yes there is a solution, no worries. But ... do you mean that you have two libraries with two sets of duplicate content on the hard drives of each PC? If you do and the reason is PC-B is a portable that you take out of your house every day - there's a workflow for that and you are missing a step and should probably change an option or two.
If they are two mostly stationary machines they should be networked regardless IMHO and a different solution/workflow applies.
And if the two PCs are sharing content found on one of the machines or a NAS, you are already networked and you shouldn't be restoring anything to the secondary PC, you should be using a shared library that can be loaded on both machines (PC-A would be the media server and PC-B would be the client) -- here I can think of two workflows that could apply.
So .... Which scenario is it? and do you actually duplicate the content on both machines or am I still misunderstanding?