When you flush your toilet, first a "bubble" of air is pushed ahead of the rushing water, then a vacuum is created behind the rush of water. And if you have one of the new "super-flush" toilets that flush in one big "fwoomp", this push and pull of air is quite strong.
As the rush of water from the toilet flush passes the junction of toilet/sink/shower drains, it's going to be pulling a vacuum behind it. If there's not sufficient venting, that vacuum will suck air past the traps in the toilet and shower (causing them to "gurgle") -- do this repeatedly and it will suck enough water out of the traps so that they no longer "seal" the trap (which would explain the "equalization" you're describing - there's now a clear air path through the trap). Additionally, if there's any sort of restriction in the drain line below (clog, low spot in a horizontal run that's pooling water, etc) the bubble of air ahead of the flush is going to "escape" up the sink and shower arms, bubbling past their traps.
From your description, it sounds like you have inadequate venting. Possible causes are-
-obstructed vent -- sometimes construction debris ends up in the DWV lines, and foreign objects sometimes end up in the vent line from the rooftop (did you reroof your house as part of the remodel? wouldn't be the first time a roofer dropped something down a vent line). A plumber (or you) can both visually inspect and run a snake down the vent from the rooftop to verify that it's clear.
-undersized vent (should be 2" for your shower/toilet/sink combo) -- an undersized vent could be further impacted by a circuitous path with lots of bends, and you'd especially see an effect with a "super-flush" toilet -- the fix is installing a proper-sized vent
-AAV (air admittance vent) - this is sort of a "ventless vent". They're normally reserved for situations like a sink in an island, where there's no way to route a normal vent. But in a remodel, plumbers will sometimes use them to avoid having to run a vent to the roof. They're a less than ideal solution - especially with high-flow fixtures like toilets and showers, because they only address the vacuum issue - they're specifically designed to close under positive pressure, so they can't vent the air pushed ahead of the flush. --- again, the fix is installing a proper sized, "real" vent
-no vent at all - the problem and solution are obvious -- install a proper vent
If you haven't made final payment to your contractor yet, DON'T! This sounds like a clear construction defect, but once you've made final payment, you may find that your builder isn't particularly motivated to fix the problem (contractor's hate fix-it callbacks -- it's unpaid work AND it takes them away from the next (paying) project they've moved on to).
As others have said, contact your GC and tell him what you're experiencing. Don't offer any diagnoses - just tell him "when I flush, I hear gurgling in the sink and shower -- if I flush repeatedly, I stop hearing gurgling and I smell sewer gas". If you haven't made final payment yet, I'd finish up with a friendly "We're excited to get the bathroom completely finished, and I'm sure you're anxious to get this fixed right away so we can make our final payment to you".
Hopefully your GC will deal with this in a prompt and professional manner (and if you haven't made final payment yet, he most likely will). But if you get any kind of a run-around about "that's just normal", "you know these old houses", etc -- you're friendly relationship with your builder has just come to an end. Be pleasant but firm, and don't accept any excuses. If he still drags his heels, tell him "So it sounds like we need to bring in a forensic plumber to run a video snake through the lines and determine what's wrong with the venting". Which is a polite way of saying "I'm putting together the documentation to sue you for faulty workmanship" and should get his attention. If he still doesn't respond, that's exactly what you'll have to do.