Reason for my original post;
1. better pictures.
2. one size fits all lens. Meaning decreasing swapping between the 2 lens I currently have.
3. Taking more pics that allows for narrow depth of field; blurring out background.
Glass makes the difference between a potentially good photo and a potentially great photo. You are correct that it is better to upgrade to better quality glass before upgrading the body. An L series lens will produce better photos on a Rebel body than my old "standard" canon glass on my 5d Mark II.
Considering you have a Rebel with a 1.6x factor, your quest for a one size fits all will not be completely achieved with a 70-200 despite it being an excellent choice. Unfortunately, your effective range will be 112-320 which leaves you with no wide angle and a "wide" beyond what would typically be used for portraits. Unless you wanted to invest in a 28-300L (the most expensive lens I have ever purchased by my "everyday" lens for 90% of my shooting) you will still need to carry a second lens.
The nifty fifty is an excellent bang for the buck. With the 1.6x factor you actually are carrying an 80mm equivalent lens which is a very good choice for portraits of your daughter. Plus, with an F2.8 you can blur the background ("bokeh") for the effect you are seeking. An F4 can give that "blurred background" effect to a certain extent but a true bokeh generally could use nothing more than 2.8 although there are ways of composing shots to compensate but that will take practice.
Lenses should be considered investments that you will keep as you upgrade bodies later on. I generally pick up a new body every 14 months since by then I have well over 100,000 shutter activations but my L lenses get constant "abuse" and keep going (with some periodic maintenance needed from such use). As a result, buy as much lens as you can afford and do so one at a time if on a "budget" (as much as you can consider L glass to be within any budget) to get something that actually fits your needs and will last you as you change bodies later on.
Unless you just want range without ultimate quality gains in your shots, I would not recommend Sigma lenses. They are fine and reasonably priced but not in the same league as L glass. Some may say that most won't notice the difference but if you want to grow with your skills you won't notice the growth with the Sigma series. Yes, Sigma and less expensive "regular" Canon glass is fine for most typical photographers but if you are intent upon trying to get a better shot and want more "keepers" then it will be in the glass.
Now understand that you still need to practice and get a handle on composition and lighting but with digital photography and photoshop it is much easier to get a good shot by the low cost of shooting a lot of photos and being able to edit with a mouse rather than a wet darkroom. There is no reason any longer to just shoot one or two frames and potentially miss a smile or a look when you can do a burst and fire off 10-20 frames where you are virtually guaranteed that one kodak moment you are looking for.
Your nifty fifty plus a 70-200 would be a good combo but you will always find that there is a situation for which you will need another lens. I know many people who rely upon the 70-200 as their "one size fits all" lens but I find it too limiting and that is why I bought my 28-300 for my first trip to the Galapagos where lens switching in the field would have been difficult to do. But, once again, that is over $2000 just for the lens so it is not for the faint of heart (or wallet).
I carry the following lenses:
16-35 L
24-70 L
85 L (F1.2)
100 L macro IS
28-300 L
100-400 L
Although the 28-300 is my "go to lens" for most shoots, I do like the 24-70 for "personal" shots such as "intimate" gatherings like a party in relatively confined spaces where I don't need a telephoto capability and could use some wide for getting the entire group in the shot. But I also have a full frame body so I get the full use of the range.
So I guess the short answer is get the fastest 70-200 you can afford since it is an investment but you will still find the need to carry a second lens mainly as a result of your 1.6x factor. Until you can get a full frame body just remember that you will always lose out on the wide end of the spectrum with every lens.
