Well normally all plumbing has a TRAP - there are a couple reasons for this - the P-TRAP fills with water and provides a barrier between the inside of the house and the outside of the house. This can prevent critters from entering (not completely but less likely), it also prevents sewer gases from entering into your home. Since yours happens to be when it is raining the sewer systems are loaded with additional water - and perhaps based on how that system is - your house is unduly affected. That said I would be investigating your plumbing for the proper installation of TRAPS.
You stated in a Bathroom and also in a living room. Where is this living room in proximity to that bathroom or other drains in the house ?
I suspect you have a missing TRAP somewhere or a blocked Vent Stack - and most probably related to that specific bathroom. Your plumber should run a camera down the drains in that bathroom and the Toilet itself, and also the VENT Stack for that bathroom - plumber should check for clogs of the vent stack or a covering - as when it rains is your vent stack becoming blocked.
Seeing as it is new construction sometimes things are blocked off during construction or debris can fall into it thereby creating a blockage. Have the plumber check it thoroughly with a camera system - snake the thing does not tell you much unless you run into something. The camera will spill the beans.