Question:As far as the collection goes, would it be wrong to take the money one would put in the collection plate every Sunday and give it to his unemployed mother, who is living with her daughter, which would be his sister, instead?
What is happening is a person is trying to play one command of God off of another. It is the same problem, just in reverse of what Jesus scolded the Pharisees for doing.
"He answered and said to them, "Why do you also transgress the commandment of God because of your tradition? For God commanded, saying, 'Honor your father and your mother'; and, 'He who curses father or mother, let him be put to death.' But you say, 'Whoever says to his father or mother, "Whatever profit you might have received from me is a gift to God" -- then he need not honor his father or mother.' Thus you have made the commandment of God of no effect by your tradition. Hypocrites! Well did Isaiah prophesy about you, saying: 'These people draw near to Me with their mouth, And honor Me with their lips, But their heart is far from Me. And in vain they worship Me, Teaching as doctrines the commandments of men.'"" (Matthew 15:3-9).
Obedience to one command is not an excuse to ignore other commands. A person has an obligation to take care of his family. "But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever" (I Timothy 5:8). And he also should be supporting the work of God.
Under Christianity there is no fix percentage that must be given, rather people give has they are able. "For if there is first a willing mind, it is accepted according to what one has, and not according to what he does not have" (II Corinthians 8:12). This is not to be taken that a Christian is spend everything he has so that there isn't anything left to give to God, but rather a practicality. Different families will have different levels of expenses in order to live. Contributions are based on a portion of the family's profit. "On the first day of the week let each one of you lay something aside, storing up as he may prosper, that there be no collections when I come" (I Corinthians 16:2).
I suspect that this isn't an either/or situation. Since the mother is living with his sister, her needs are probably low. So, he probably can send some money to help her out and probably will have some funds that he can give to the Lord as well and still be able to live comfortably on the remainder. He can also help his mother out by helping her apply for whatever financial aid is available from other sources, such as the government.