There may be a stamp duty clawback if when your wife purchased it was in last 5 years AND she availed of a lower rate of stamp duty ie a first time buyer rate or an owner occupier rate at the time AND that house now ceases to be her principal private residence (which is the case if you are moving to the new house).
There is nothing preventing her retaining the property but you should consider not just stamp duty implications but also Capital gains tax -cgt. If the house has gone up in value since she bought then any profit on a sale now is tax free but if she holds onto it for a few years and then sold only a portion of the profit is tax free.This is usually offset by the additional gains made while property prices are rising as in last few years but if the market were to stagnate that would not be the case. Its really a question of balancing all the pros and cons.
My understanding is that you,in all likelihood ,will not be able to avail of FTB status now particularly if your wife is contributing directly or indirectly to the purchase