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Until what age is it permitted to see one's own daughter nude? 3? 12?
What about prayers - how does one behave if during Amidah, or any other prayer or brochos, she is in front, with naked butt? Or even if she carries her potty, trying to sit nearby to be in her zone of comfort? Does one need to keep distance, and turn back, or what?
I think you are asking about three separate issues
You are welcome to edit your question if somehow you wanted to ask for different things. Briefly,
1. Until what age can one see one's daughter nude?
I don't believe there is an issue for a mother to see her daughter nude but don't have sources handy. There is no issue of Yichud (being secluded alone) between a father/daughter or mother/son (SA Even HaEzer Siman 22:1) although I am pretty sure it is not appropriate for a father to see his daughter nude past the age of bat mitzva (but don't have sources here). I will edit if others can help with sources.
2. Can one pray in front of a naked child?
One may not discuss Torah or other holy matters in the sight of genitals, neither his own nor another person’s, even a child’s. (The one obvious exception is at a brit mila)
Closing one’s eyes is not sufficient so long as it is in front of him; rather, a person should turn away so that he is no longer facing the nudity. The Rema rules that in a case of need, we may be lenient when in sight of the nudity of a boy under nine or a girl under three (OC 75:4)
Note that turning away, or even moving if needed, is allowed during amida. Speaking however is not allowed. See here for details.
3. Can one pray near a toilet/potty?
You can pray near a toilet/potty which is in a different room, e.g., near a bathroom with an open door but in all cases you must be four amot from the source of foul odors and not see tzo'ah. See here for details. So in your case it appears you can continue to pray if she brings her potty but not if she starts using it.
For practical rulings remember to CYLOR.
