Hi Waynezo,
Below are some items to check or do that may solve the problem for you.
Please don't feel insulted if these are things you've tried already. Most are to be done with the power off to the indoor unit and the outdoor unit at the circuit breaker(s) or fuse(s).
Please also pardon that the list is long & pretty much boring to read. I wanted to give you as much to check on your own as possible to save the cost of a service call.
Hopefully others will stop by and add to the list things I forgot.
Paul
A) Check the indoor unit (usually furnace) filter. Make sure it's clean. Also, high MERV rating can sometimes cause lower cooling efficiency due to the restriction. A MERV of 7 or 8 is good for most situations.
B) Check the indoor fan for dirt partly clogging the air flow. It builds on the blades of the fan. When a filter gets a little dirty (or is a high MERV one) air sneaks around it and clogs the fan blades.
C) Clean the condensing coil. It is outside surrounding the outdoor unit. Usually washing it with a medium force spray from a garden hose is sufficient. Spraying it with a spray bottle with gentle dish soap & water before rinsing helps. (Never use glass cleaner. Ammonia eats aluminum and copper)
If you can, lift the lid off of the condensing unit and spray the coils from inside to out. Clean debris from the bottom (won't help cooling, but will slow rust).
D) This one may be difficult: If you can somehow access the evaporator coil (it is most likely above the furnace), wash it. Wash carefully so the water lands in and drains out of the drain pans. Sometimes, this is a more tenacious dirt than outside. Evaporator coil cleaning sprays are available. No-Rinse ones exist.
E) Check for air leaks or restrictions in ducts. Do a mirror & flashlight check to see if they are packed with dirt (doubtful)
F) After doing all of these things, run the unit for an hour or more on a humid day. One of the refrigerant lines is a larger diameter than the other. It is the Suction Line. Pull back some insulation. Check for condensation on the line. Check for temperature. It should be cooler than the surrounding air near the furnace and have some condensation on it within minutes of pulling back the insulation. If it stays dry and warm, you may have a problem that requires a service technician's diagnosis. She will check the charge level & fix leaks, she'll check superheat and sub-cooling. She'll investigate for restrictions.
TEMPERATURE DIFFERENCE-
You mentioned a temperature difference between outdoor temperature and the vent. Unfortunately, those locations aren't a very helpful gauge.
The more valid way to check is the temperature difference between air going in to the evaporator coil and out of the coil. This is called the "Delta Temperature" (or "Delta-T" by the hipsters). Measurements are done within a few inches of the coil.
What is correct depends on a whole lot of variables. A whole lot. (Primarily the expansion device you have, the refrigerant in use, the weight of the air and the temperature will dictate what the delta temperature should be.)
I am not a residential guy (chillers and absorption units mostly) but have heard what is called the "Lazy Rule" stating that 15 to 20-F difference is correct for a house unit. Others say 10- 15.
There are charts on line, but be careful of which one you use so that it matches your type of equipment. Example: My house unit operates on the Bernoulli Principle, therefore the delta is often 48-F or more, so that would not be valid on yours. Chillers can have a delta-temp over 100-F. So study carefully.
MINI-SPLIT-
Your idea of a mini-split is a very good one even if your air conditioning works well. You can save money by using only the small unit on moderate days. And, as you suggested, it can supplement on hot days.
DEHUMIDIFIER-
It won't cool the house faster. (Actually, it'll add heat from its own condenser.) But, as Tee-Square mentioned, drier air feels cooler. (Drier air does hold less heat, but the air conditioner will dry faster and more efficiently.)
AWAY-SETTING or SET BACK THERMOSTAT-
Some thermostats have Away Settings where the unit is off or set really warm while you're gone. They can cause more problems than needed if set wrong. When you return, the machine has to not only de-humidify & cool the air, it has to de-humidify and cool all the objects in the building. I don't know what the ideal set-back temp is for air conditioning, but your local utility probably has a good article on the subject.
SWAMP COOLER-
Lots of people have asked me about swamp coolers that they see advertised on TV. (Fan blowing across a damp sponge or filter) They are good for low humidity areas like parts of Arizona because the damp air will evaporate off of your skin making you feel cooler. It'll make you miserable in Florida.