Need new tires all around 12 volt john deer tractor and 1 and reverse gear dont work good

Donna, there could be an issue in the transaxle/gear box take it into a good small engine repair shop and have them diagnose and estimate repair. Check the attached links,instruction and guides, Good luck
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John deere riding mower l120 has no reverse
John Deere SX 85 will not go into reverse or move backwards
Riding Mower Will Not Go In Reverse Quick Fix

add an additional 6 volt power wheel battery in series with the 12 or even use two 12 volts see you tube for examples

have some one activate it while you feel it if you feel a click or movement its working if not its bad then get a volt meter set to 12 volts ceck the voltage going to it 1 ground 1 hot if its grounded to frame it may have only 1 hot wire when its activated

check your oil , there is a sensor that well keep it from working if the oil is to low ( a little low is all it takes to ruin your day)

bad motor, let me know if you need me to order you a new one

cables might be switched around on the shifter switch

check tha battery and charger with a multimeter and make sure they are showing at least 12 volts

bad motor, you can get a new one here www.powerwheelsoutlet.com

do both wheels spin in 1st gear?

GO ON LINE TO JOHN DEERE PARTS YOU CAN DOWN LOAD PARTS DIAGRAMS AND WIRING DIAGRAMS ALSO. CHECK THE PLUGS AN THE WIRING HARNESS AND MAKE SURE THEY ARE CLEAN. WITH A VOLT METER YOU CAN CHECK AND SEE WHAT VOLTAGE YOU ARE GETTING TO THAT RELAY. I DON'T HAVE A DIAGRAM TO LOOK AT BUT IF I CAN FIND ONE ONLINE I'LL LET YOU KNOW. HAVE YOU CHECKED FOR A SECOND RELAY