1. The husband is responsible for maintaining the wife by providing basic provisions such as food, drink, clothing, accommodation, cash for personal needs, etc.
If these rights are all taken care of and you possess surplus funds (as you have indicated in your query that you are of a good financial standing) then you should certainly spend and fulfill the needs of your widowed mother as well. Both the wife and the mother enjoy rights over you which should be fulfilled in a manner that one is not oppressed in trying to fulfill the rights of the other, but the rights of both should be fulfilled. Being a medical consultant, we assume that this can be easily achieved (due to your financial position).
2. The wife cannot prohibit you from spending on your mother more especially when her rights are being fulfilled.
3. You are not responsible for supporting your wife’s family. However, if they are financially unstable and you are able to financially assist them then you should and you would be greatly rewarded for that Insha-Allah.