Religion has really fucked up my family.
I'm sorry to hear that. This is one of the overlooked tragedies of religion, the bad guidance that causes so many people to walk off a cliff. I don't know if you can help her or not. Sounds like the moving thing is locked in. Maybe you can offer her better guidance. Maybe she'll take some of it at some point in the future. Maybe if you can't help her, you can still help your brothers and sisters.
Is there any way to convince her that tithing isn't necessary from a biblical perspective?"
Possibly. Probably not. But possibly.
If you want a statement that christians are supposed to tithe or a statement that christians are not supposed to tithe, you'll need to look somewhere besides the bible or get into some long distance extrapolation from bible verses.
If you decide to go the route of arguing that tithing is not biblically necessary, there are quite a few examples she could retreat to where the bible is strongly in favor of tithing or tithing-like concepts (the commandment to give 10% to the Levite priests, Paul shaking down the corinthians, the bit in Malachi about the storehouse of the lord, the unstated but pretty obvious subtext of Ananias and Sapphira, bringing the 'firstfruits', lots of glowing mention of people making sacrifices to god and how much god likes it when people make sacrifices to him, etc). The other bad news on this front is that most churches will have already done that extrapolation and they will have more explicitly pro-tithing policies than their claimed source text. If she is already willing to accept her pastor's interpretation of scripture, she's probably already convinced that tithing is biblically necessary.
So it's a hard sell. But convincing her not to base her decisions on the bible would be a longer fight than convincing her the church is acting in an unchristian manner (no guarantee that even this is possible).
Points available to you include:
1) The modern christian practice of tithing is not described anywhere in the bible, let alone commanded.
2) What does god need with a starship (obviously this one isn't biblical (it's from Star Trek) but if one posits an omnipotent god then it's a valid point)?
3) Jesus only ever mentions tithing to illustrate the hypocrisy of the pharisees (his statements here are not exactly anti-tithing, but more along the lines of "you think you're righteous cause you make the tithe but God would prefer if you were actually righteous").
4) In most of it's earliest explained forms (earliest in canonical order, not necessarily chronological order) a sacrifice is meant to atone for one's sins. If the sacrifice of Jesus atoned for your mother's sins, what's she paying this other guy for.
5) Much of the exhortation to giving is not phrased as "give to the church" but rather "give to the poor". To most of the new testament authors besides Paul, it appears that tithing-like concepts were closely tied to providing for orphans and widows. When Jesus is speaking to the rich man in Matthew 19, he says "go and sell that thou hast, and give to the poor". In Acts 2:44-45, a communal system is described wherein everyone gives what they have to a common pool which provides for the needs of all. That's a very different practice than what happens in churches today.
6) When Jesus rebukes the religious hierarchy for their hypocrisy (Matthew 23, the same chapter as "ye pay tithe of mint and anise and cummin, and have omitted the weightier matters of the law, judgment, mercy, and faith"), one of the charges he makes against them is "ye devour widows' houses". Considering the particulars of your mother's situation, this seems rather applicable. It could at least plant the suggestion that preachers fleecing the disadvantaged is not something Jesus would be down with.
Subliminal factors to consider include self-preservation and decorum. If she were convinced that not tithing wasn't wrong, you could expect some internal rationalization toward keeping the money. If she decided on keeping the money and felt the eyes of the congregation on her when the offering plate was passed, you could expect her to feel immense pressure to tithe.
I hate to say this, but the grasping preacher scenario Custador mentioned is basically how I see this playing out (although most of the churches I've been to didn't have mandatory tithes, just offering plates and lots of pro-tithing rhetoric).