Yumeji-San
I'm not certain if you can marry someone after abandoning another marriage (without divorce). But, it wouldn't make much of a difference. A ring isn't going to physically bring them back. A marriage certificate isn't going to keep them true to you. I guess I just see marriage as something pointless, unless you want some income/business perks.
Although, I am curious, my mother said I was registered as Roman Catholic, thus if I can only marry once in a Catholic church. I'm not certain if this is true/still practiced? I believe the only excuse was to get the Pope's permission. But if I'm personally atheist, would this still apply [or does the registration conflict with this]?
You can marry again if you get a divorce from a previous marriage. You have to (be divorced, have possesion of a decree absolute) by law or it counts as bigamy, which is illegal.
I think your mother is right. Most churches will let you marry in them once but it is up to the individual church. Some have no problem with re-marrying, some will turn you away.
If you are athiest then I wouldn't think about a church wedding. It's a little hypocritical to marry in the "House of God" when you don't believe in him and some churches will request that you are a regular church goer sometime before your wedding. If that makes sense....