Question for atheists, straight from my mom.

I am an atheist and I frequently have theological discussions with my mom. She's an avid Christian, and dislikes my non-belief but has not been confrontational or wildly emotional. That being said, she is interested in "steering me back," as they say, and when we discuss, she always uses one specific point to try to argue why she believes in God.

Point #1: People pretty much believe a guy named Jesus existed. Theists and atheists alike.

Point #2: There are multiple accounts from right after he died that corroborate his story.

Point #3: These guys who wrote the accounts risked their lives and were often put to death for telling the "truth." Why would they do that unless God was real and Jesus was who he said he was?

I've tried researching this but I get a lot of crap that I can't sift through. Everyone is so biased and everyone has their own sources, and point #3 has me stumped. Why WOULD they do that? Did they?

Gah, so tired of debating this back and forth and back and forth. Just exhausting. In my heart, I don't feel the presence of God. And God's absence from Earth and his tendency to allow kids to die of starvation kinda makes me not like him, if he is real. I don't even know, man.

Tl;dr - My mom says God must exist because the men who wrote about Jesus risked their lives, why would they do that unless they really saw Jesus get resurrected, therefore, blah blah blah. Help?

Edit: The points you guys are making, these are the points I made. Lots of people die for stuff that they think is true, the accounts of Jesus' existence weren't contemporary, another thing I would ask is do you think the disciples were real? Did their accounts happen at all?

Edit 2: Thanks you guys. You've given me some great talking points to bring up with my mom. I appreciate it.