Both the EF 70-200mm f/2.8L IS USM and EF 70-200mm f/2.8L IS II USM lenses are great lenses. The EF 70-200mm f/2.8L IS II USM lens newly incorporates a fluorite lens element and includes five UD (ultra-low dispersion) elements, one more than than the EF 70-200mm f/2.8L IS USM lens. This does improve overall image quality.
Another benefit of the EF 70-200mm f/2.8L IS II USM lens is that it is a lens that is still in service life. Our repair facility would be able to repair it in case it needs to be sent in for repair. The original EF 70-200mm f/2.8L IS USM lens has reached the end of its service life to where parts are no longer manufactured for it and the repair facility is no longer repairing this model.
There is no doubt the EF 70-200mm f/2.8L IS II USM lens is a great lens. It may be the best 70-200mm zoom lens made. Period! If you have to have the best of the best that is it.
However, if I were a Rebel T6i owner I would opt for the Canon EF 70-200mm f/4L IS II USM Lens. If you don't need f2.8 you should check this a lens out. Two big reasons, one is it is lighter to work better with a Rebel and two, it is a whole lot cheaper. The best part I doubt you will see or even be able to tell any difference in IQ.
When I owned several Rebel cameras I used the f4 lens myself. Remember f4 to f2.8 is just one stop.
This tool lets you compare the two model lenses.
The Version II is better. Depending on your primary shooting subjects it probably isn't noticeable in the real world.
The biggest consideration to me would be the service life issue that JacobT mentioned. Third party repair options might be available should it ever be needed.
You can balance the facts against the cost differential.
I have owned and used the EF 70-200mm f/4, 70-200mm f/2.8 IS, and 70-200mm f/2.8 IS II. The EF 70-200mm f/2.8 IS (version one) is a good lens but in my experience it is the least sharp of all the f/2.8 versions, and less sharp than the EF 70-200mm f/4 IS. I would say it is on par with the f/4 non-IS.
If you are on a budget, I would also consider the original EF 70-200mm f/2.8 (non-IS) as it is a very sharp lens, and IS is not critical when shooting sports.
I have the EF 70-200 MkII IS USM units in the f/2.8 and f/4 versions - they both produce outstanding results. However, for someone for whom weight is going to be an issue, then the f/4 is definitely the way to go. It is MUCH lighter than the f/2.8: 780g vs 1.5kg, so roughly half the weight. They say the best camera (and lens) is the one you are prepared to carry. If your wife is going to be a major user of the lens, she will thank you for the fatigue she will avoid in avoiding what is a bit of f/2.8 brick, and as one fatigues, then the ability to manage a camera degrades.