Frankly, I would not worry about losing a limb if you are going to be in a tank. Usually, you either make it out, or you don't, and you are either burnt, half burnt, or not burnt. Just don't stick anything but your head out of the tank, and you should not lose your limb (... and stay alive, that is). So... 6 combinations basically.
How to convince your parents? Financial during ROTC would be one. Prestigeous school (as in better than the ones you could get in if not for ROTC) could be two. Telling them you would not come back without a limb (which is kind of true....

) would be three. Discipline / training could be four. Threathen to sign up without their support could be five.
As for whether there have really been a lot of potential attacks on your country... really... I don't think that many people believe it, at least not the non-Americans. First of all, next to none of the "terrorists" are really convicted. Under most definition, that only make them suspects, not offenders. Secondly, those drill they do in airports and such... the homeland security always mess up on those. If the underover agents could carry a bomb and pass through security, how could they catch the real ones? :? Thirdly, and I probably should not say this, but... seriously, there are quite a number of lapses in the securities they have implemented. But then, we are not here to discuss that are we? Anyway, above are 5 ways you could consider to try and "convince" your parents, but if I have kids, I would never let them sign up.
Oh... and for your cousins husband... sometimes it is not that easy to get another job. First, there is the contract one signed, which at times have a specific minimum period attached to it. Then, one has to consider the qualifications and the skills one has. Lastly, opportunities and market situations may not be well for his qualifications and skills. There are a lot of people out there in jobs that they don't like but can't change due to different reasons, including high-pay (in relative to their qualifications), job security, contracts (and the penalty if they don't finish it), routines (ie. uncertainty in getting, and performing in a new job)... etc. The socialization (or re-education, or brain-washing, or "boot-camp", whatever you want to call it) is also another influence, because some people view quitting as un-manly, and quitting as deserting their pals (which are some values that are particularly prevalent in military).
But anyway, don't view us as trying to deter you. We are just trying to give you an all-round view in the reality of the military. One of my prof. is a former navy commander (for AWAC planes, or survelliance, or whatever...) and from what he has said (not even in a negative sense), the military is not as glorious as it appears. Office politics, inter-departmental competitions... etc. all exist in the organization that is supposed to be defending the country. However, those darker secrets play roles often as well and power struggles are considerations during operations.
Please take us seriously and go do more researches with an open mind. If you find you truely like it, you could find the faults of the military and come up with counter point before your parents bring those faults up. You could impress them with your maturity and show them you have thought this out well and thoroughly. That would help convince them in addition to the above 5 points. If, however, at anytime you have possible doubts about the organization, you could always look at other opportunities as well. Researches aren't going to harm you, that is for sure.