OK so having read through the thread. Here are the comments I have about your situation as a young lady who has traveled internationally quite a bit and is currently living overseas:
1) You seem to be quite fearful. Unless she is going to a war zone or somewhere where there is a disease epidemic (or has some sort of medical condition or food allergy that she needs to have close supervision of), there simply isn't a good reason to think she is significantly increasing her chances of death by going overseas. Hundreds if not thousands of people go on short term missions trips every year, the vast majority of them come back safe and sound and have no need for medical treatment while abroad (and you can by travel medical insurance fairly cheaply to cover that eventuality). Despite the waivers you sign deaths and injuries are quite rare.
2) Sounds like your wife may be having a difficult time adjusting to having hours at home with no kids around. You make it sound like she is doing a bazillion and one different things to try to fill up her time or maybe find some significance. Africa isn't going to solve this restlessness, but if it's the underlying factor in her desire to go, it is definitely worth talking about.
3) The fact that she signed up for an overseas trip either without talking to you about it or against your wishes is one of those red flags that all is not well in your relationship. This is the kind of thing that you should be talking about and in agreement on. Best thing you can do for both of you is go LISTEN to your wife. Unless you've been silent its a pretty good bet she knows you don't want her to go. So find out why she needs this so badly she is willing to defy you over it. Be humble about it because the trip is not the issue at this point; that you are willing to care for her and see to her needs and want her to know just how much you love and appreciate her and hate that this thing is causing friction is the real issue.
One other thing to discuss are the practical logistics of how the kids will be cared for, how what she usually does will get done during the two weeks she's away. Not knowing your wife she may have it all planned out already, or she may be caught up in an emotional high of "doing something big to serve God" and not have thought about the practicalities, but I will agree that it is still part of her responsibility as wife and mother to make sure this stuff is covered while she is away.
I'd also second the advice to talk to the trip leaders, both because they can probably reassure about the safety and security stuff they have in place, and because they should be aware of how much of a division this trip is causing in your marriage. I hope you can both get things worked out and come to agreement and be a stronger couple for it.
1) You seem to be quite fearful. Unless she is going to a war zone or somewhere where there is a disease epidemic (or has some sort of medical condition or food allergy that she needs to have close supervision of), there simply isn't a good reason to think she is significantly increasing her chances of death by going overseas. Hundreds if not thousands of people go on short term missions trips every year, the vast majority of them come back safe and sound and have no need for medical treatment while abroad (and you can by travel medical insurance fairly cheaply to cover that eventuality). Despite the waivers you sign deaths and injuries are quite rare.
2) Sounds like your wife may be having a difficult time adjusting to having hours at home with no kids around. You make it sound like she is doing a bazillion and one different things to try to fill up her time or maybe find some significance. Africa isn't going to solve this restlessness, but if it's the underlying factor in her desire to go, it is definitely worth talking about.
3) The fact that she signed up for an overseas trip either without talking to you about it or against your wishes is one of those red flags that all is not well in your relationship. This is the kind of thing that you should be talking about and in agreement on. Best thing you can do for both of you is go LISTEN to your wife. Unless you've been silent its a pretty good bet she knows you don't want her to go. So find out why she needs this so badly she is willing to defy you over it. Be humble about it because the trip is not the issue at this point; that you are willing to care for her and see to her needs and want her to know just how much you love and appreciate her and hate that this thing is causing friction is the real issue.
One other thing to discuss are the practical logistics of how the kids will be cared for, how what she usually does will get done during the two weeks she's away. Not knowing your wife she may have it all planned out already, or she may be caught up in an emotional high of "doing something big to serve God" and not have thought about the practicalities, but I will agree that it is still part of her responsibility as wife and mother to make sure this stuff is covered while she is away.
I'd also second the advice to talk to the trip leaders, both because they can probably reassure about the safety and security stuff they have in place, and because they should be aware of how much of a division this trip is causing in your marriage. I hope you can both get things worked out and come to agreement and be a stronger couple for it.
we only know one side to the story... and sacrifice is different from your calling... nuns, priest, etc... they felt in their spirit that they were called to step into those roles. If we look at Abraham and Isaac, what was permanent about that? Her walk with God is different from ours and although I strongly believe in submission, I also believe in discernment. We need to look at the bigger picture.... is she going on a vacation? No.... is she going to have an affair? no.... all we Know is that the OP is concerned about he's wife coming to Africa on missionary work and he has the right to be cause that is the woman he loves.... But he needs to ask himself, are her actions bring glory to God? Will she be saving lives in the name of God? Are my needs greater than the needs of God? 
