Is it wrong for me to give my mother everything she asks for, including large sums of money and other things, when this causes problems with my wife?

The rights of parents are great, and being dutiful to them is an obligation. A person's spending on them is among the foremost expenditures and carries the greatest reward, especially if they are poor. Buying luxuries for them is not obligatory, but it is an act of kindness for which one is rewarded. The wife has no right to object to the husband's expenditures on his parents and his dutifulness to them, as long as he is fulfilling the obligatory spending on her and their children, unless there is extravagance or squandering of money involved, in which case the son should not assist. Spending for the pleasure of Allah brings replacement and expansion of sustenance, and Allah replaces what is spent by the spender.