Electrician has wired a 14/3 to the ceiling fan with two switches on the wall for light and fan.

Hampton Bat remote has (2) wires B & W in with (3) wires W,B,Blue out.

If I wire the 14/3 straight to the fan(blue to red), (black to black), (white to white) wall switches works but I lose remote capabilities.

If I wire 14/3 (black and white) to the remote (cap red), remote works but wall switches (light portion) does not work.

Is there a way for the wall switch to work (controls light and fan) as well as the remote.

With your setup you can use the wall switch or the remote but to use one control the other control must be on. This can becoming confusing and isn't how we nirmallly set up a fan with remote.

In answer to your question, no. You cannot use the remote AND both switches.

Ceiling fan wiring - Ceiling Fans N More