First off, no matter what you do to cover and patch the 'problem', it will most likely return unless the proper & long-term measures are taken to stop the moisture problem.
By simply 'covering up' the damaged concrete and insulating & vapor-barriering the wall, you only put a bandaid on a bleeding wound. The dehumidifier will remove the moisture AFTER it's already gotten into the basement. If this is going to be a livable space for your daughter, you might also want to check w/your insurance company to see if you live in a 'flood plain'. If so, will your insurance cover any damage due to flood (since you mentioned it.) If not, I wouldn't even take my chances because of the potential future losses. (You say your funds aren't great, and if your insurance company won't cover any damage, you most likely can't afford to repair any damage and replace any belongings in a flooded basement.)
Aside from a basement moisture problem, if the basement wall is damaged to the point where it will compromise the structural support of the house above, again, patching won't 'fix' this problem. So, although a contractor can patch the wall, it may NOT be the 'solution' to any problems in the future when it comes to support. He or a Structural Engineer may need to assess the situation. No one on this Forum can do that.
You or your contractor may have to remove any 'wall covering', like drywall, to assess what's behind it especially if there's visible damage leading up to it. No one in their prudent mind would overlook this likelyhood. And if you have damage leading up to the finished wall, and a contractor DOESN'T want to remove the drywall, I'd find another contractor. To me, he's obviously overlooking 'something' in the name of saving you some $$$. The important thing in your particular situation is to get the RIGHT estimate for now and FORGET about the cost so you can see what damage you have AND what it would cost to fix it. THEN, you can decide to either just 'fix' the problem w/o finishing off the basement for your daughter, or 2) fix AND finish off the basement for habitation. From the sounds of it, you need to also consider heating and (possibly) cooling this room, and adding lights and a new/updated bathroom.
What I suggest is you get 2 types of SEPARATE estimates. 1 estimate is to just fix the basement problems, structurally and water/moisture-wise. The 2nd estimate is to finish/upgrade/improve the basement for living. DO check w/your insurance company to see if they'll cover any existing damage AND a possible livable basement. DO consult a Structural Engineer (or a reputable contractor) to assess the wall and moisture issue(s). I'll tell you now that it will cost some $$$ to just have the situation assessed. Again, you talk about 'funds are not great' but at least spend some $$$ on having the basement looked at. At some point, you may sell your house and its value will be dramatically reduced if the problem(s) aren't rectified. Besides, later on, it may cost MORE to fix than it would now. At least now, you'd know where you stand.