If I understand your idea, then I see some really big problems.

1. The inbound spacecraft is going very fast. By the time it hits the Earth's atmosphere, it'll be doing somewhere around 25,000 MPH (at least, that's how fast the Apollo spacecraft were going).

2. In order for the outbound spacecraft to rendevous with the inbound spacecraft, you'd have to launch it on a very high parabolic trajectory. At the apogee, the outbound spacecraft would be going quite slow, perhaps just a few thousand MPH depending on the apogee.

3. The outbound spacecraft would then have to match courses with the inbound spacecraft and then accelerate to match the velocity. Some of the acceleration would come from the Earth's gravitational attraction but most of it would have to come from propellants.

4. By the time you've accelerated fast enough to match velocity with the incoming spacecraft (and perhaps even faster if you have to catch it from behind), you no longer need to bother with exchange energy. Problem is, even if you rendevoused with the incoming spacecraft, you aren't exchanging energy with it. Instead, you're just matching its kinetic and potential energy.

As Gary pointed out, "simply" getting the crew home alive is challenging enough without having to add the complexity of performing a high speed rendevous under those conditions. This seems like a good case for KISS engineering.