I just wanted to add a note here for you as well. You sound like a decent husband and a loving father, and I applaud you for loving your wife just as she is. You don't mention how old she is, but I'm assuming she isn't terribly old considering the ages of your children. I've been married to my husband now for going on 22 years, and he's a great guy, most of the time. He's not rail thin, but he's not really big, either. He's pretty average, and IMHO, he's handsome and still looks great for his 53 years.
I'm going on 49 and was born into this world one roll at a time. VERY fat baby! Unfortunately, it stuck with me my whole life, and I come from a very long line of very tall and VERY fat people. My mother died at the age of 66 from complications of diabetes, renal failure, and heart disease. The last twenty years of her life, especially the last five, were a horrendous parade of doctors, dialysis, illness and misery. By the time she passed, she had lost all her toes, most of her skin, and she was almost blind, all from diabetes. At her heaviest, she weighed well over 500 lbs. She was very self conscious about it and rarely went anywhere she didn't have to, leaving my dad to go and do things by himself or with his friends. I've also done this myself for the same reason, as I have also been over 500 lbs myself. It sucks.
If your wife has a shot in hell of not living this reality, PLEASE let her have it. Don't stand in her way. I would have given anything to have had my mother able to come to my school stuff and be able to sit in the auditorium. Because she couldn't, she didn't let me go, either, so I missed out on most of my own childhood. I was careful not to do that to my daughter and went and endured he stares, whispers, snickering and pointing, but it was hard. As a woman, it's heartbreaking when you can't do things that you need to with your kids. I was never able to get outside and play with my daughter like I should have when she was small. She's 18 now and I missed all of that. Don't do that to your wife. Once these years are gone, she won't be able to get them back or get a do-over.
I wish I'd had the chance to have the surgery when I was younger so my skin would have been more elastic and tightened back up better. At my age, it's all just saggy! And on a more personal note, once the fat is gone around certain areas, things are much easier to stimulate and reach, so the bedroom department will only improve!
I understand about your concern for your wife being there for you and your children, about how inconvenient it's going to be for you to have to step up and handle things for a bit while she recovers. and about you wanting to finish your degree and this being a distraction for you. If she does this, you're also going to be losing your eating buddy, and maybe you're afraid she will start in on you to lose weight or see you in a different light once she's smaller. Men will probably look at her and treat her differently, which will suck for you and raise more insecurities for you about the strength of your relationship. But this isn't all about you.
If she's determined that this is the best thing for her, the best thing you can do for YOURSELF is be as supportive as you can be and help her through it, and pray for her if you're a believer. If you fight her every step of the way and make her feel like she's got anything less than 110% of your love and support, then if she does go through with it, all your worst nightmares will probably come to fruition. One of the biggest side effects of this process is divorce, and it usually happens because the spouse is either non-supportive, or has been an ass throughout the marriage, and once the wls helps restore self esteem and self confidence, and the ability to be self sufficient, suddenly that non-supportive ass of a spouse is no longer looking all that appealing. Don't let that be you.