Our car runs ok but gets a hot smell and a rotten egg smell comes out the exhaust

Clogged exhaust or over rich fuel mixture.

Well your rotten egg smell and your run issue is usually caused by a plugged-bad cat.convertor.

that smell is usually a sign of the catalytic converter which is the first wide muffler looking thing under the engine after the first pipe from the engine.

it is happen to old engine because the oil that escape from the engine(engine cover near the exhaust) when it is got hot it sends bad smell but after how many minutes if it already dried up because of heat it will gone (like frying using the used cooking oil in pan there is a different smell).

REMOVE UPSTREAM 02 SENSOR INSTALL VACCUM/PRESURE GAUGE START VEHICLE IF THERE IS MORE THAN 1 PSI EXHAUST HAS A RESTRICTION, CAT/MUFFLER/COLASPED IN EXHAUST PIPE INTERNALLY

If car runs okay with egg smell, its normal and working the way it should, if car is running poorly and the rotten egg smell has gotten worse, its a sign that your exhaust catalytic converter will need to be replaced. good luck!

The rotten egg smell if it is coming from the exhaust is a very good sign that you catalytic converter has failed or is failing. but a bad or battery that is being overcharged can also make a rotten egg like smell.

Not sure if engine coolant smells like rotten egs when it burns inside the cylinders , but it sounds like you may have blown a head gasket. Coolant and/or oil could be getting inside combustion chamber. Another possibility is that the catyletic converter might have broken up and colapsed onto the screen where it goes into the exhaust. Might give the rotten egg smell and block the exhaust enough to cause backpressure sufficient to cause the engine to run poorly too.
Try putting your palm over the exhaust pipe , if the exhaust is coming out in pulses (pop ,pop,pop) thats normal , if it is just slowly flowing out with no noticable pulses , I would check into the cat converter problem.

The engine is running rich, find what is causing the rich run and that will fix the rotten egg smell

Make sure she is using the correct octain gas; not any higher as it can endup in the cat and smell bad and damage the emission system.