Carrots123
There is no way that Robb will become a puppet as mentioned earlier Robb's position as king is secure and even the Targaryen supporters won't back her over him so he is not in any way giving Daenerys the kingdom. Also while yes the Tyrells supported Robb earlier they didn't do it out of the goodness of their hearts they did so to make Maegery queen. Both Robb and Maegery understand this while they might have come to care for each other they are by any means in love. With regards to your final point regarding the heir to the Throne, yes that could cause problems but I suppose they'll simply go with the first born son which in my opinion will be better if it's Daenerys son as he'll have the claim of two royal houses both the old and new as well as inheriting Deanery's dragons who will be much older and bigger by them making his position more secure than a Tyrell heir who would then have siblings that ride dragons.
Marrying her is actually the best and most realistic option as Tyrion clearly explained, if she joined Aegon Robb will have to face an army of Fifty thousand as well as three dragons, what ever plans he might have made to fight the dragons had a good chance of failing, even if they managed to kill one it is doubtful they could kill the rest the same way, even if they succeeded the cost would be ruinous. the best thing Robb can do is to find a way to divide duties amongst the two wives, if Daenerys decides to retain her holdings in Essoss and incorporate them into the kingdom then it is likely she would focus more on that than managing the castle and playing politics which Maegery is more suited to
But she is sterile so I know after losing her son the witch cursed her, because there is a problem and only the position of queen remains, the tyrels would not accept such a marriage and according to the sacred law of the 7 such a relationship is prohibited from what I understand there are 2 problems without religious acceptance and their strongest allies hmm
Marriage with Danaerys is also the same as giving the kingdom Rob has build to her as if they were both married the power scale of the king and Danaerys will shift in favor of her which due to lack of trust in the king or for favor of dragons rob will lose his supporters, this will cause her to be more dominant in the court making her the ruler and rob the puppet that gave her the kingdom.
Marrying with two people will make the heir to the crown so muddy as the first born from either queen can assume the thrown or will try assume the thrown plus it will make a division in the kingdom court which in turn make a new game of thrones after Rob is dead so having two queen is not good political decision.