The Interactive Diagram can enforce a limit of one Tsarevna at the time by initially puting one Tsarevna in hand, letting captured pieces go to the hand of the owner, and specifying the Tsarevna must come from the hand in promoChoice. It could enforce maximally three times promotion to Tsarevna by having it come from the hand, and putting three of them initially there, without returning them on capture. But it cannot enforce both at once.
The thee times rule seems completely pointless, though. I understand you want to create a possibility that one has to checkmate with two Frogs, but this rule is very unlikely to do it. The Tsarevna is a strong piece, and promotion to it will have a large probability of being decisive. The probability that a game would not yet been decided after three such promotions is vanishingly small. To have any effect, the limit on promotion to Tsarevna should be lowered to one. Otherwise you might as well not have any limit at all.
The Interactive Diagram can enforce a limit of one Tsarevna at the time by initially puting one Tsarevna in hand, letting captured pieces go to the hand of the owner, and specifying the Tsarevna must come from the hand in promoChoice. It could enforce maximally three times promotion to Tsarevna by having it come from the hand, and putting three of them initially there, without returning them on capture. But it cannot enforce both at once.
The thee times rule seems completely pointless, though. I understand you want to create a possibility that one has to checkmate with two Frogs, but this rule is very unlikely to do it. The Tsarevna is a strong piece, and promotion to it will have a large probability of being decisive. The probability that a game would not yet been decided after three such promotions is vanishingly small. To have any effect, the limit on promotion to Tsarevna should be lowered to one. Otherwise you might as well not have any limit at all.