If you don't have a lease at the old place by the time you move to temporary place, you should file AR-11 and I-865 noting your temporary place address. Then another AR-11 and I-865 when you move again.
The online portion only takes 2 minutes to file, so no issue there.
There can be a problem if you use either current or temporary address on I-751. USCIS sometimes ignores any address changes and sends correspondence including GC to old address. Mail forwarding generally doesn't work for GC and other docs sent by USCIS.
So, the best course of action is to file I-751 using new long term address if your wife is still going to be within 90 days window of filing at that point.
So if you're moving in to permanent address before deadline in March, just file I-751 from that place.
It's better to file from stable address VS rush and file from old or temporary one.
Considering I-751 takes 2+ years on average, a month or two later or earlier won't make any significant difference to processing time, but will ensure GC is safe and will arrive at the right address.
VJ has many stories of one's I-751 getting derailed because of moving in the process. People don't receive RFEs, NOIDs, interview letters because of moving.