Could you say a little more about your signal chain? Guitar > Mic > Preamp > Dynamics > effects > recorder, etc.
Avoid pointing the mic directly at the guitar's sound hole. Try aiming for the area where the neck meets the body. You might also insert an EQ during tracking and drop several db in the 100-200 hz range. Or, check your mic to see if it has a switch to cut at the low end. If your signal is clipping, you might benefit by inserting a compressor.
It's also possible that some of your sound issues can be addressed during mixing. Banjos, guitars, and dobros exhibit a lot of overlapping frequencies and sometimes you need to carve out space for each instrument by using an EQ. You might also accomplish the same thing by altering the arrangement. Try not to play lead parts on all the instruments at the same time. Use the approach that bluegrass bands often take: one guy at a time steps up to the mic, plays lead and then backs off. Depending on your style, you can also "squeeze" the guitar in between the banjo and dobro by playing bass runs instead of full-blown chords.
(INSERT SMILE HERE: The only weapon in the war against those nasty resonator instruments is the D-28! Or should I say the D-$2,800)