"The unit has to slide back with no access so I don't think copper is an option." You put a loop or two of copper tubing as large as you can fit behind the unit. Pull the loops out like a large spring to connect up (do NOT straighten the tubing) or pull any further than you need. After making the final connection yo simply push the unit back in. The coils of copper will collapse back down between the unit and the wall and not be any thicker than the plastic tubing you are trying to use.

Captainbob the plumber here, I am assuming you have a shut off valve on the hose, before the hand sprayer. You must have what is called a vacuum breaker built into your hose faucet on the wall. It is a one way valve that allows water to flow out of the faucet and into the hose, but not back from the hose into the faucet, sort a 'safety valve' to keep contaminated water from getting back into the water pipes in your house. It can be an annoying side effect of the set up you have. For some reason there must be pressure building up in the hose greater than what is coming out of your faucet, or there is a water hammer reaction happening when you open that valve and open and close the hand sprayer. I've seen it many times. Or, it could be the vacuum breaker/hose combo is defective that your plumber put in. If the faucet is not defective, replacing the wall faucet/vacuum breaker combo will not necessarily solve the problem, unless you have one put on that does not have a vacuum breaker in it. They are probably required by code in your area. Your plumber should be able to tell you this. I don't know if I would recommend leaving the hose faucet on all the time, maybe extending it out would be better, or be creative with your gardening and create an opening to get at it. Good luck, Captainbob the plumber

There are basically three methods used to mount the angle stop valves. 1. Solder type 2. 1/2"NPT Thread mount 3. 5/8" compression mount. In new construction the angle stops are generally installed during the final trim out phase of the plumbing, which generally occurs after the painting or wall finishing phase. At this stage there is a very high risk of causing damage to the wall finish if we were to install the solder on type or to solder a thread adapter on the stub out. For this reason most plumbers elect to use the 5/8" compression type which only requires a simple mechanical connection. To install the compression type angle stops the stub out is cut to the desired length, then the compression nut is slide on the stub out, followed by the brass ferrule and finally the valve is slipped on. With the valve held firmly in its final location, the ferrule and compression nut is then slide out to the valve and tightened finger tight. Once the compression nut is finger tight the plumber uses two wrenches, one to hold the valve steady while the second wrench is used to tighten the compression nut. As the compression nut is tightened the inner brass ferrule is slightly compressed into the wall of the copper pipe thereby locking it firmly in place. When changing compression mount angle stops many people make the mistake of attempting to pull the ferrule and old nut off the copper stub out and usually in doing so they distort the shape of the copper making it very difficult to get a tight seal with the new nut and ferrule. A much simpler and more reliable method is to unscrew the compression nut then slide the old valve off the copper pipe leaving the original ferrule and compression nut on the pipe. You then remove the compression nut and ferrule from the new valve and slide the new valve on the pipe, tightening it in place with the original nut. While this method does not work 100% of the time, as a rule it will work most of the time and certainly bears trying before you begin cutting the pipe or trying to remove the old ferrule. When tightening the compression nut you can use a pair of channel locks to hold the valve steady, but when doing so be sure to pad the valve with a rag first so the teeth of the channel locks does not scratch the finish. I find an open end wrench to most convenient to tighten the nuts in a tight space. (I especially prefer my Craftsman ratcheting open end wrench.) When selecting angle stop valves I use the solid brass 1/4 turn ball valves exclusively. The ball valves have the advantage that they are quick acting full bore valves and they are also have the advantage that when turned they are self cleaning which is a distinct advantage in areas where mineral scale builds up on internal valve parts. I will probably open a real can of worms here, but My first choice of supply lines is chrome plated brass tubing with the cone washers that come supplied in your faucet set and the compression nut and ferrule that comes supplied with your new angle stops. I have seen copper or brass tubing supply lines that have been in continuous service in commercial applications for 20 or 30 years and they still work fine. My absolute last choice would be the stainless steel brain lines. While the stainless steel braid gives the illusion of being some kind of high tech space age strength and durability in the final analysis many of those lines are the absolute weakest link of all the choices. It is true that the stainless steel braid will prevent a line from blowing out, but when we consider that the maximum allowable line pressure is 85psig, the chances of any lines actually blowing out is slim to none. On the other hand, what most people don't know is that a vast majority of those stainless steel braid lines has nothing more than a stainless steel braid over a cheap neoprene hose. Under certain water conditions neoprene has a relatively short service life as is evidence by the failure rate of neoprene toilet flapper valves. In regions where they have problems with the water deteriorating the neoprene I prefer to use chrome plated brass lines with the factory preformed cone washers that are made out of nylon.

"until I can get back to it with some more experienced eyes guiding me" You did the right thing by stopping before you messed it up so that noone can fix it.