I figure I can help. Flooring is sort of in my blood so to speak and I spent more than my fair share of time carpet bagging.
You are looking at roughly 112 sq. yds. based on your estimate that said, your mother in law has you figured at just a tick about $60/sq.yd. That would get you some of the higher end carpets and upgraded pad for sure, some carpet that I wouldn't exactly call "living grade" more like that one room that no one goes in grade. One brand that comes to mind is Masland, but I think you should be just fine and more than happy with a nice Shaw or Mohawk carpet.
The real question is here what are you looking to get for the floor? If it is going to be a rental or a flip then you might want to go with a decent lower mid-range carpet. Seeing as it is a rather large townhouse and you probably want to get a good tenant who is going to respect the place (at least a little) and get you a fair dollar for rent, you will likely want to spring for a bit more than the cheap shit. For the same token you don't want to kill prospective buyers for the flip with a really low grade carpet.
Obviously some carpet is going to wear better than others, I'd suggest for longevity go with a nice cut pile or a berber. Don't forget don't go cheap on the pad - get yourself at least a nice 8-10lb pad. Figure that will run you about $5-6 sq.yd for a really decent pad.
You can probably save some money by rip up and removal of the old carpet. Do a good clean job here and you will have yourself some happy installers on the day of the new carpet install. Remove the old tackless strip (if it is old and needs replacing) and after you remove the pad, take the extra 20 mins or so and remove the old staples that were holding the pad down. An ice scraper/floor scraper could help you here or use a flat head screwdriver to slide under the staple and pull them out. Clean sweep up and a nice shop vac job and your good to go.
Remember if you have to deal with stairs things can get more expensive for the install as they are going to charge you for things such as capping the step if it is open on one side or both and any spindles for the banister if you have any of that. Can get to be like $8-9 per step. If you do the rip out on the steps do a real clean job - sometimes when they cap the steps they use a ton of small staples to finish under the "flapped" cap part.
With all that said, tackle the rip up and removal yourself. Grab a buddy and some beers and take to it - do a clean job and you will save yourself some money. I think you should be able to get it all done for about $5-6k for some really nice carpet - I am talking some carpet you'd be happy to live in a house with. If it is a rental or a flip then I think you could probably do some shopping around and get out the door for around $4500. Choose the store and installer wisely, be sure to get references or a possible look at a past job or two, it would be unfortunate to have a nice carpet ruined by a less than professional install - be picky!