In many classes, I get asked, "Larry, what should we do when they use a Convention (such as CAPPALLETTI, or DONT against our Strong Notrump?) There is no fast answer. To cope with interference, you need to do a little studying and memorizing. (Otherwise, be prepared for some accidents). You and your partner have to come to some agreements.
It is impractical (unless you are a world-class bridge pro) to try to memorize different schemes versus different methods. For example, to play System-A against DONT, but System-B against CAPPALLETTI, and System-C against Brozel would be too much memory drain.
Here is a simple scheme to deal with any kind of interference--you can choose parts or all of it. For a more complete (and more difficult scheme), click here.
If they double 1NT (as a convention), don't even bother asking what the ALERT means. Just ignore them. I mean I-G-N-O-R-E! All your bids mean what they would have meant without the artificial double. If 2 would be a transfer, then it is still a transfer. If 2NT would be a transfer then it is still a transfer. Just pretend they passed.
[If they PENALTY Double 1NT, then just play ALL NATURAL -- no Stayman, no Transfers. Use XX as a rescue/runout]
They Bid 2
You can also ignore ALL 2 overcalls. You double to say, "They stole my bid." So, double is Stayman. All other calls mean what they would have meant if the opponent had passed.
They Bid 2 or Higher
If they overcall 2 or higher, I suggest you abandon transfers completely. Bid naturally (and if you know lebensohl, you can use it). Play DOUBLE as "negative." It would take too long to explain exactly what qualifies as "negative." But, here is a simple explanation: It is NOT penalty. It is not purely showing the other major(s). It just means, "Partner, I have values to bid, but no bid I can conveniently make."
This scheme is not 100% complete, but it will help you cope with most situations with a minimal amount of memory strain. If you want a more thorough treatment, click here (but I warn you to be prepared for a headache).