"Would having two antennas connected, one through PCB trace and other through direct SMA cable be a problem for the performance of the device?"
Absolutely. RF is a fickle creature and having stubs on a PCB is a good way of having neither antenna work.
However, all is not lost. The Hittite/ADI HMC849 is designed to switch between antennas and is not too expensive. If you need it to automatically switch, try detecting any DC current to the external (active) antenna. More than about 2mA and you can safely say an external antenna is plugged in.
Antennas are reciprocal - they transmit and receive equally well (or poorly).
The reason it's important to tune a transmit antenna is because a mistuned antenna, by reflecting power, can destroy the transmitter output stage.
Tuning a receive antenna is much less important, compared to that!
Most receive antenna tuning is frequency sensitive, in fact in the crystal set days, the antenna was often part of the first tuned circuit, and re-tuned for each new station.
With a broadband antenna, there's really not much point making such adjustments.
However you can improve reception by:
if the received signal is weak, increase its height, or use a larger antenna better suited to that waveband.
if it's strong but contains interference, use a directional antenna to reduce the interference - or add a tuned circuit to reject the interfering frequency.
and so on.
These can make big differences in reception. If we knew what you are specifically interested in receiving, you may get more specific answers.
Best Answer
I believe the component you are looking for is called an RF switch. They are used for example for switching the TX path of bluetooth and wifi chips to a single antenna. RF switches are quite inexpensive (relative term, I know), and come for many purposes.
The terminology for RF switch classifications is similar to regular switches, i.e. SPDT means single-pole-dual-throw, i.e. a single common signal can be routed to two locations.
Here's a relatively generic one which works over a relatively large frequency band (incl. GPS) http://fi.mouser.com/ProductDetail/Skyworks-Solutions-Inc/SKY13270-92LF/?qs=sGAEpiMZZMtsfndvJ9ArQ1GAoWUJ3yIM3lKzNTG0W6Y%3d
Datasheet: http://www.mouser.com/ds/2/472/200128G-23362.pdf
Please note that RF switches are nowadays often minuscule components and can be difficult to solder manually for the unexperienced.
Here's a more generic article about RF switches by digikey: http://www.digikey.com/en/articles/techzone/2012/aug/rf-switches-simplify-multi-antenna-systems