Can you combine two existing stations in openTTD

I believe the straight forward answer is "no"; as you've discovered the load/unload orders you can give to vehicles currently do not allow you to make them ignore the cargo they have dropped off.

However, as a work-around, have you considered a single combined station instead of a feeder service?

Assuming the bank is close enough to the airport (dependent on your settings, more below), you can Ctrl+Click when placing a loading bay (or equivalent) near the bank, and select an existing near-by station (i.e., your airport) to have the new construction form exactly the same station. Then they share waiting all cargo, ratings, etc - so there is then no need of a feeder service.

The maximum spread of a station is an advanced setting that you can change, and defaults to 12. I'm fairly sure it can be adjusted mid-game, if necessary.

At present, AIs are exclusively for competition. This is probably in part because OpenTTD, more so than its progenitors, is a multiplayer game, and giving players access to that kind of automated tools would damage game balance.

There might exist patches that'll let you offload certain aspects onto AIs, but that carries with it its own set of problems (compatibility with trunk saves, for one, and also the fact that quite a few patches appear in one version, remain supported for a few version, and then wither).

Additionally, half the fun of a game like OpenTTD is all the micromanagement. ;)

Side note:

One patch designed to alleviate some micromanagement issues, albeit in a different maner from what you describe, is cargodist, which is well-supported and popular, but the above notes on versions and support still applies.