Without a schematic of what you're dealing with it is very difficult to advise you.
However, if these two sinks are side-by-side bathroom vanity sinks, then they should need only one shared trap and one vent after the trap.
The easiest thing to do is to install an air admittance valve under the sink base after the trap, IF allowed by your local building code.
Check out www.studor.net about AAVs. Studor is a well-known worldwide brand name,
Then call your local building inspection department to see if AAVs are allowed in your jurisdiction. They are easy to install right after the trap under the sink with basic plumbing skills.
The alternative, if AAVs are NOT allowed, is to run a 2" pipe from a T in the wall behind the sink base with the trap draining into the T (and a 2" vent going up to a 2" connection to a 4" fitting installed in the vent pipe going up through the roof). The T will allow the water to drain in and downward and the air to come in from the top to vent it.