First off that's really awesome to be helping like that! I have heard it helps eczema sometimes. I think as you may know it can take time, and sometimes it is in conjunction with cutting wheat etc too.
But in any case - storing kefir past a week (flavored) is kinda hard. It never spoils, it just gets higher alcohol, sometimes more bitter or more sour too. Whatever you put in it (strawberry banana is always a fail safe flavor with kefir that kids usually love)...is going to speed up the ferment too. It won't be dangerous to eat, just more fermented and higher alcohol as time goes on. Which isn't horrible, it just may be a bit off-putting to the toddler (or not who knows!).
Kefir can make good popsicles (if they have plastic molds to pour it into)! Probiotics are cut some, but there's still a good amount left. And consumption doesn't have to be huge anyways to benefit, especially for a 3 yr old, a 1/4 cup once a day is great. My toddler started drinking it around 1 (I think?) and loved it plain, but usually doesn't want more than 1/4-1/2 cup. Some people feel that breaks are beneficial too so I wouldn't worry about it having to be something in her diet every day. Hope that helps some!!
Oh and if not I'd try your hand at a veggie ferment as that stores for much longer - only problem is whether she'd like it or not! pickl-it has a site dedicated to this.