As per previous, the actual requires you to register TM30 each time you re-enter the country if staying in private accommodation, even if you own it. However, the owner of the property ( in this case your wife ) is actially responsible for doing it, and can be fined if they do not.
if you only ever use hotels and they take a copy of your passport, they will do the TM30, so in this case you do not need to.
Supposedly, if you travel around Thailand, you should report to each area immigration office you intend to stay in, if there is not one available, then the local police station.
However, my local immigration office, Jomtiem, informed me when i asked, that i only need to register if i leave the country and return. That was last year. The chief immigratoin officer is now implying that this bit is not correct and we should report at each province etc.
i will have to go and check at immigration again.
of course, the problem is always that various immigration offices interpret the rules differently.
i guess, in order to be fine free, it is better to register everywhere you go.