Hello, A few things that might interfere with airflow are the dryer and the flue connecting both water heater and furnace. Some furnaces have a powered vent, or a fan in the vent. The water heater is probably atmospheric draft, so only uses the buoyancy of hot flue gasses to drive the venting. If the furnace has a blower in it, that will easily overpower the water heater and prevent it from drafting/venting correctly. If the room is closed up when the dryer runs, it could be pulling air down the water heater’s vent, preventing the water heater from drafting as it should. I’d be tempted to sit and watch the water heater’s flame with both the furnace and dryer turned on and off to see if these things have any affect on the water heater.
Beyond that, it would be useful to see a photo of the control for the water heater, so we might be able to help figure out what adjustments it has and where.
ps, Is the water heater natural gas or propane?