Thank you for your post.
Yours is not an uncommon situation for managing patients who have extensive prior treatment experiences.
The previous presence of the M184I/V mutations implies that such 3TC or FTC-resistant virus are archived in the patient's potential viral population. Hence, the one can reliably predict that when 3TC or FTC is resumed that the full potency of the 3 drug regimen may be compromized.
If there is no other drug resistance, it's possible that the combination of meds in Atripla could retain potentcy; this is theoretical, since M184 mutation-harboring virus tend to actually increase the susceptibility to tenofovir (and AZT).
However, because of the so-called low genetic barrier to the selection of subsequent resistance to tenfovir and efavirenz, the risk of failure in this patient is higher than in the treatment naive, fully drug susceptible patient. Given this, if she were my patient, I'd tend to consider the use of medications with higher resistance barriers to partner with a 2 NRTI (or NNRTI backbone)- boosted PIs in particular.
I hope this helps. BY