I can't believe you're going back...
Why? We had a great time, loved the food, people, culture etc. Also it is a growth area in our professional fields!
your wife is going to stay indoors nearly all the time?
Not likely, she is the Scientific Attaché for the French Embassy... She got the job, and as an acadmic scientist (biophysicist/biochemist) it was not too difficult for me to find another lab there to continue my research (muscle disease in children)... So, it is not as though I’m dragging her there, nor do I think it will be a problem. 
Of all the countries I've been to, I've never been harassed and treated as badly as I have in India. And I'm male. For women travelling alone, it is worse again.
When I was in India, I got a lotttT of the "a white guy! he's 'rich' let's try to get some money out of him" in tourist-ee areas, but it got pretty repetitive (and extremely funny..) after like 2 days.. . It wasss annoying when people would try to get in my pictures, though.. (They then expect you to "tip" them..) But they'd do it for *everyone* with a camera.. DSLR or not. That was about the extent of harassment I got.
There were definitely some sketchy people, but I think they pretty much gravitate toward alll tourists, in terms of "easy money", and I never felt any sense of danger. It was fairly innocent attention. I also started telling them off pretty quick, and they left me alone, since they knew they weren't going to get my rupees! It was as easy as that.
(However, there are things like people-who-watch-your-shoes-for-money... And they do that for EVERYONE, not just "whitey", so in those cases you really should be paying them.)
I did get loads and loads of kids coming up to me asking for hand outs (because I'm white).. At first it was annoying, and they would keep pestering me, but I had brought a lot of gum, so I started handing sticks of gum out, and they couldn't have been happier. : D No more pestering, just lots of happy kids, and they'd either want to talk to me, asking me lots of questions, follow me around curiously, or move on and get money from other people, depending on how touristy or busy the area was. An older woman asked me for money once, as I was giving gum to some kids, so I offered her a piece, but she just gave me a dirty look, hahaha.. So I gave her some money, and THEN she reeeeally wanted the gum, too. : D
Outside of tourist-ee areas, I got a whole lot more interest and excitement just by being a foreigner. People were very warm and friendly, and if I had my camera out, they loved to get their picture taken and see the results on a screen. (This was 5-6 years ago, though.) No idea how it's changed since then..
Also, as for weather, Rajasthan and Bangalore are totally different beasts, I think? Rajasthan was hot and dry, and was just fine.. (46 degrees c (115+ f) - no problem!). Sure you might sweat, but you won't be soaked in it (especially carrying around a camera bag). Hopefully Bangalore isn't has humid as Chennai! In Chennai, it was instant-soakage and it did NOT leave you. Oh man! Loose clothes and loose bags. The temps weren't nearly as hot, but the humidity was a killer.
Also, if I was stomping through heavily packed areas, like a bazaar, I wouldn't have my DSLR out, though.. Just my point-and-shoot in my pocket. Mostly because, as someone mentioned above, the DSLR really gets in the way. I guess if you're more aggressive and/or gung-ho you can get out there in the thick of it, but that really isn't my style, haha. : D
I WAS paranoid of thieves trying to lift stuff from my backpack, though... I didn't have a backpack camera bag, though.. just one at my side, and i had the zipper / flap pointed IN toward my body, so there was pretty much no way anyone could get into my bag (short of cutting it open, I guess, but I wasn't THAT paranoid, hehe..)
As for those lenses, I'd normally recommend the 70-200 over the other two, but in your case, I'm not sure.. I don't know the 70-300 size/weight.. if it's significantly smaller, mayyybe.. but I doubt it is, though I have no experience with that 70-300. I have the 70-300 IS NON L and I also have the 55-250 ef-s. I brought the 70-300 IS non L with me to India (the 55-250 didn't exist then), and it was great and I used it a bunch, but I don't think it really has much over the 55-250, other than full-frame coverage (which you don't have, so it's a non-issue..). The 70-300 IS non L isn't quite as sharp at 300 as the rest of the focal range, so that extra 50mm reeeally doesn't get you much over the 55-250.. I would say it's not worth it. And its autofocus speed isn't anything to write home about, if I recall, though I've never actually tried comparing it to the 55-250. Buttt, I don't think I've ever tried to use the 70-300 for anything that neeeeeeded ultra autofocus, so it's never let me down, either.. (None of these lenses are really birding lenses..) And since I know that range, personally I wouldn't bother limiting myself with the 70-300 L 5.6, when I can get the 70-200 II 2.8 and throw a 2x adapter on there for 400 5.6 if I reeally needed it (except for autofocus speed, perhaps... I'm sure the adapter will kick it below the belt in terms of autofocus, but I've never used that lens with an adapter, so I don't know.). But that's just me. So I'd say stick with the 55-250 or go all out with the 70-200. Maybe give the 55-250 a shot over there, even though its falling apart.. The 55-250 I think is an awesome everyday stomping around telephoto.
Sounds like an awesome experience for you guys! Enjoy it! : D
