After divorcing my wife with a first, revocable divorce, and then taking her back, and then divorcing her again a year later with a second, revocable divorce, do I only have one divorce remaining with which to take her back, and is anything required for me to take her back now?

If a wife has been divorced twice, she can be taken back (reinstated) before the expiration of her waiting period (iddah (definition)) by saying: "I take back my wife" or similar words. The iddah ends with three menstrual cycles for a menstruating woman, with childbirth for a pregnant woman, and with three months for a non-menstruating woman. If her waiting period from the last divorce has not ended, then reinstatement is possible; otherwise, there is no way except through a new marriage contract.