A sister plate is a US name for a patch plate I gather ?
As mentioned before, weld the crack all the way round with the frame strongly clamped to prevent warping
Now grind the welds back flush
Over the top of the weld, put in a patch plate of steel at least 1/2 the thickness of the frame steel and do a full fillet weld around each plate
If you can not put a plate on one side, then don't grind back the weld on that side.
IF done properly it will be twice as strong as the original frame.
heck the same position n the other side of the mower for a similar crack.
You might have gotten a mower with a frame problem from new or you could have a balance problem causing excessive vibrations leading to the cracking.
Cracks don't just happen they are caused.