Fox Collectors

I bought my 16 ga 2yrs. but it has taken that much time due to snags to get it finished. My questions:
1. I loaded 2 shells then fired the right barrel and it doubled on me because the sear for the back trigger wouldn't hold. I finally found a sear and got it installed. Now that it is installed everything works but the front trigger has a harder trigger pull then the back trigger with the new sear?
2. Also, My stock man pointed out the side movement of the triggers is around 3/32". Should I install new triggers?

Your sears/hammer notches need to be reworked for the appropriate trigger pulls.

Some play side to side with the triggers is relatively normal. 3/32" is very excessive and touching on impossible, so I would question the accuracy of that measurement. You likely have no issue here to address.