There is a problem and it is not a good idea to do that and your Kiddushin might be no good. However, if you do the Kiddushin, give her the ring and then stop do something. Take a picture, to wait a minute, or wait till after they read the Ketubah, then she can give you the ring if she wants to and say something about you being her husband, etc. That should be fine.
The Gemara in Kiddushin 5b writes halakhot in greater detail. The Sages taught in a Baraita (Tosefta 1:1): How is betrothal performed through money? If a man gave a woman money or an item worth money, and he said to her: You are hereby betrothed [Mekudeshet] to me, or: You are hereby betrothed [Me’oreset] to me, or: You are to me as a wife, then she is betrothed. But if she is the one who gave the money to him, and she said: I am hereby betrothed [Mekudeshet] to you, or: I am hereby betrothed [me’oreset] to you, or: I am hereby to you as a wife, then she is not betrothed.
Rav Pappa objects to this: The first part of the Baraita states: If a man gave a woman money and said to her: You are hereby betrothed to me that the reason the woman is betrothed is that he gave her money and he said the appropriate formula. Therefore, if he gave her money and she said the formula, she is not betrothed. Now the latter clause of the Baraita: But if she is the one who gave the money to him, and she said: I am hereby betrothed to you, then it is not a valid betrothal. Rav Pappa infers: The reason that it is not a valid betrothal is that she gave money to him and she said the appropriate formula, from which it may be inferred that if he gave money to her and she said the appropriate formula, then this is a valid betrothal.
The Gemara explains: The first clause of the Baraita is exact, and therefore it is correct to infer from it. By contrast, the latter clause of the Baraita was cited for no reason, i.e., it was simply formulated in the opposite manner of the first clause, and the Baraita is not exact in the wording of this case. Therefore, one should not analyze this clause too carefully and infer halakhot from it. The Gemara asks: And would the Baraita teach in the latter clause a matter that contradicts the first clause?
Rather, the Gemara retracts, this is what the Baraita is saying: If he gave the money and he said the formula, it is obvious that it is a valid betrothal. If he gave the money and she said the formula, it is considered as though she gave the money and she said the formula, and therefore it is not a valid betrothal. And if you wish, say a different explanation of the Baraita: If he gave the money and he said the formula, she is betrothed. If she gave the money and she said the formula, she is not betrothed at all. If he gave the money and she said the formula, the ruling is uncertain, and by rabbinic law, we are concerned that this might actually be a betrothal.
Rashi explains that when the husband gives her money or Kiddushin this is what the Torah says Ki Yikach Ish, the man takes a woman. However, if the bride says after he gives the ring “I am married to you “then it is as if the woman brings herself to him, not him taking her. This is not what the Torah tells us how things are done.
According to the second statement of the Gemara, if he gives the ring as he says the Mekudeshet part, it’s a doubt if the Kiddushin is good.
The Poskim argue what who to understand the Gemara:
The Rambam in Hilchot Ishut 3:32 rules that is an unclear Kiddushin. The Rif, however, says we are concerned for a Kiddushin Derabbanan.
The Shulchan Aruch in Even HaEzer 27 rules like the Rambam that it is a Safek Kiddushin when he gave and she said, unless they were discussing getting married beforehand then he gave her the ring then they are definitely married.
The Sefer Sheilat Moshe is not sure in this case why is she even married at all. Is it because this Kiddushin is missing the Man’s active taking of the woman? That is since he needs to say Harei At Mekudeshet Li , and it was only half a Kiddushin, and she finished the Kiddushin and he has to do the whole thing from beginning to end. Another possibility is she says Harei Ani Mekudeshet, she is nullifying his action and she is taking over the Kiddushin. The difference is if he gives a ring and says Harei at Mekudushet Li and the woman gives a ring to the man and says ‘Hareini Mekudeshet Lecha”. According to the first reason, there is complete action of the man, giving and saying the proper words, what happens afterward doesn’t matter. However according to the second reason, one could say that her act of giving the ring nullifies his action. So when she gives the ring and says Hareini Mekudeshet Lach, it nullifies his Kiddushin and they are not married
The Sheilat Moshe concludes that she would be married properly if she says I am Mekudeshet to you. However, if she says “Harei Atah Mekduesh Li”, meaning she is intending to do Kiddushin and “take her husband “ to her it might nullify the Kiddushin. He is uncertain.
The Lev Aryeh as well is not sure in the case where the women has the intent to do a Kiddushin to her husband does it ruin the Kiddushin or is it just foolishness and ceremony and meaningless and has no bearing on the Kiddushin. He is also unsure.
In conclusion, in our case, it is better not to do a double-ring ceremony. To avoid fights etc. then the groom must give his ring first and say Harei At Mekudeshet Li. After she takes the ring, the Kiddushin is finished. Make a separation between his giving and her giving, for example, take a picture, say Mazel Tov, wait a minute, do the Kriat Ketubah and then she may give the ring and say Harei Attah Mekudash or whatever she wants to make everyone happy. Then it definitely meaningless.