Recently, my shower water does not get hot(lukewarm at best) unless the washing machine is on its beginning cycle. Once the washer has filled with water, the hot water at the shower goes away. So whenever we want a shower, we have to do a load of laundry and run to the bathroom for a 3 minute shower. I have no idea what could be causing this... any suggestions?

Is this a new problem or has it been ongoing for some time? Has any work been done on your plumbing lately? If you can think of nothing the you could cap off the hot line and loop a new hot supply over from the 3/4" hot water main. Good luck, Tom

Is the washer using hot, cold or warm water.
How is hot water pressure and flow at other faucets?
What kind of shower valve do you have?

This only makes sense if the washer is filling with cold and your shower valve is partially blocked on the hot inlet. Answer Tom and Harold's questions and we'll try a few things. I think we are going to have you pull that cartridge out of the shower valve in the end.