I have a home with an in ground septic system, it normally works great; however during periods of heavy rain the toilet nearest the discharge either flushes very slowly or not at all. The upstairs toilet as well as the guest bathroom across the house (farthest from the septic system) work fine even when it rains hard. My question is: can I fix this slow flushing toilet by installing a grinder pump inline outside in a pit between the home discharge pipe and the inlet pipe to the system tank?

The septic drain field is flooded by rain water so the nearest toilet has the least amount of pipe for the flush to be contained in. That's why the upstairs and guest toilets can flush, more empty pipe. This may be an indication that your system is beginning to fail and may need to be replaced. Check where your roof gutters are going. Make sure that surface drainage is diverted from the leachfield area. Call a professional septic inspector if your not sure of the conditions but a pump will not correct what you have described.
Mark
Maine Site Evaluations, LLC