We have a small bath with shower noticed a very putrid door from it a few weeks after we moved in. Not sewer gas. Have had plumbers come in. No one can find the source. Changed toilet. But gets bad w.hen we use the shower. No leaks found. What can we do. Do we have to rip it all out and change every thing

First of all you can eliminate the toilet. The only way you can get an sewer odor form a toilet is if there is no water in the bowl or there is no wax ring or a defective wax ring and there is a partial blockage.

That leaves the tub and the lavatory drains, the incoming water and some other source.
If the odor is only present when using the tub that eliminates the incoming water and some other unknown source. If it were the incoming water, the odor would be present when using the lavatory and when using water in other parts of the house. If it were some other unknown source the odor would be present all the time. Granted it might be more noticeable when using the shower because of the increase of heat and humidity.

Close the tub and lavatory drains. Fill the tub using the shower head. If there is no odor you have again eliminated the incoming water and the "some other source". If there is an odor, look for the "some other source". If it were the incoming water the odor would be present when using the lavatory and in other parts of the house.

Assuming no odor while filling and after filling the tub, the odor must be coming from the tub or lavatory drain. Open the tub drain while keeping the lavatory drain close. If there is an odor while draining and after draining the tub, the odor is coming from the tub drain.
If there is not odor, close tub drain and refill tub. This time drain the tub with the lavatory drain ope. If there is an odor, the odor is coming from the lavatory drain.

After determining which drain, remove the stopper and clean the drain using a zip snake shown below. The odor is probably coming from decaying hair and soap scum in the trap.

If you determine that odor is coming from some other unknown source (present all the time), close both the tub and lavatory drains. If that eliminates the odor you have a trap being siphoned dry. A trap being siphoned dry would mean a blocked vent pipe.

Barbmark,
What material is your shower base made of? Often, custom shower bases, that are tile on top of a mud - set, will have issues with moisture accumulating between the mud set and vinyl / rubber liner; this condition will result in odors / fumes...

Sickly sweet to me means dead animal, at the early stage of decomp anyway.