I think the best way to approach the situation is for you or your wife, or both of you, to talk to each of her parents separately. Ask them how they feel about the separation and their current living situation. Ask them if they really do want to get back together, why they want to get back together, and what might be stopping them from pursuing that. Then, ask if they feel comfortable bringing it up with their former spouse. Offer to approach the spouse with them if they feel more comfortable that way. Encourage them to keep the conversation casual and not put too much pressure on it too soon. Perhaps they could schedule a date-like activity for them to just spend time together, whether or not they broach the topic at that time. Encourage them to keep spending time together, for it will help them decide whether getting back together is what they want to do.
It sounds like another big part of the equation is your wife. It sounds like she really wants them to get back together, so make sure to communicate with her openly through all of this so that she maintains reasonable expectations. Be there for her if her parents decide not to get back together and she's disappointed.
Also, when you're talking to your in-laws, remember to keep the focus on them, and not what you and your wife are hoping for. Help them decide what the best course of action is for each of them and for their relationship.