Hi P.,
First, I would like to say that it seems your wife has a very supporting and loving husband! It is so good to see a man that is willing to ask for help for his wife if she's too shy to ask herself!
Now, on to the heart of the matter. I'm going to share my experience. Your wife is not alone with the breastfeeding difficulty.
I wanted to breastfeed exclusively, and tried in vain until my son was 6 weeks old. We had latching problems, and I felt very stressed out and like a failure because I couldn't breastfeed properly. I began to resent having to breastfeed- being chained to the house. After the third to fourth week, I pumped the breastmilk frequently throughout the day and fed my son the breastmilk in the bottles -- but then a couple weeks after that I was so aggravated because I spent so much time pumping, just to turn around and give him a bottle - it was so time consuming. I'd just break down crying because I felt like a failure as a new mother. During my pregnancy, I had considered giving my son up for adoption because I was going to be a single mom - so I started second guessing myself ("I can't even feed my own baby right, maybe I should have given him up"). When I realized I felt resentful towards my son for not being able to latch... I decided right then and there I needed to do something different.
I chose to stop breastfeeding and give my son formula. We tried a few different kinds, and ended up using Similac plus Iron. I bought powder because the ready-to-use liquid was so expensive. He never had an issue with spitting it up, but some of the other brands made him gassy.
I felt guilty at first for not breastfeeding -- every parenting organization seems to push it on you - like it's the only right thing to do. After a couple of days, I realized the stress over trying to breastfeed was gone and I wasn't resenting myself for my inability - and I wasn't resenting my son at all. I was much happier, and since I had been shy about feeding in public, too, it relieved so much anxiety (which I think had led to the latching problems and to much of the stress). I travelled with bottles full of sterile water, and pre-measured the powder formula into little tupperware containers. I could warm the water a bit in the microwave, then add the powder, or warm the bottle in a pan, bowl, or sinkful of hot water. My five year old son only occasionally gets colds, has had only one or two ear infections (and he has short eustachian tubes so is more prone to them!). He just started Kindergarten and is far ahead of his peers - most of who can't even recognize the letters of the alphabet muchless write them -- my son has been writing his letters for a year or so. He can already add (though hasnt memorized the addition facts yet), and is reading simple sentences. ("Jane see spot run. Spot runs down the hill"). He frequently uses words such as "dangerous", "disappointed", "competition", and "forcefully" in everyday conversation -- and uses them correctly and can tell me what they mean. Breastfed or Formula fed doesn't make a child better or smarter -- I've been working with my son since he was a few months old and I believe that is why he knows so much! He's just as healthy as other children his age - and honestly getting sick once in awhile is a good thing as it gives the immune system a chance to test itself -- and once a child is exposed to something, s/he will make her/his own antibodies against it.
The bottom line is this: it is not going to do your wife any good or your child any good if your wife is stressed out about feeding. This time with your child only comes once. If your extended families harass her about it -- then both of you need to stand firm on whatever your decision is -- and tell them that you appreciate their concern, but you feel you are doing what's right for your child and your family (wife/you/baby) - and politely deflect futher comments or advice. I hope you and your wife find the solution that works best for you -- whether it's breastfeeding at home and bottlefeeding in public, exclusively breastfeeding, exclusively formula feeding, or something else.