Ideally your sister would remove all dairy products until she felt your niece was no longer having symptoms at all. At that point she could do trials of butter, yogurt, cheese, etc to see what is tolerated and what isn't.
As far as the connection with a speech delay - I think it really depends on exactly what's causing the delay. For example - in the case of my 12 month old - she was a projectile vomitter from about 2 weeks old (as soon as she was nursing enough to actually vomit). As a result she developed reflux pain and would arch incessantly - as the OT we consulted explained - to get away from the pain. The arching led to her having "high tone" in which her muscles were not balanced well which led to her having an uncoordinated tongue movement and suck which led to difficulty nursing. She gradually improved to the point where she can now nurse effectively although unconventionally - she still arches during a let down so my nipple is stretched as far as it will go. But now she has been slow to progress on solids, has difficulty getting into a quaduped position (all 4s) so crawling is also unconventional, and I fully expect delayed speech. In this case the answer in addition to getting rid of the food intolerances causing the reflux, is playing with her an positions that encourage more normal muscle tone. A different baby whose speech delay is similarly connected to the food intolerance may have a totally different path of getting there, yk? So this probably doesn't give you anything useful. But I found it incredibly helpful to consult with other people. This convoluted story above I never would have figured out on my own. It took consulting with LC's, OT's, ST's, chiropractors, and MD's, and all the smart Mamas on MDC to figure this out.
If your niece is having a speech delay at 2 1/2 I would strongly advocate for an EI eval, if she isn't already getting services.