Intermittent internet service in Las Vegas

We moved to a new neighborhood in June 2013 and since that time we have had weeks of functional internet service followed by random hours or days of no internet service.  I cannot count how many Cox employees or Cox contractors have been here and changed out the connectors or replace the splitter in the smart panel.  Sunday night we lost service again.  I called and was told it was maintenance.  At 8 pm on a Sunday night?  That made no sense.  On Tuesday we lost service again.  I called I think four times that day and rebooted a dozen times.  The first CSR told me that  maintenance is not done at peak times on Sunday night; I was misinformed by the third-party phone answerer on Sunday.  He got us working again for  a short time.  More disconnections and two more calls resulting in short term success.  After the fourth call, in which the CSR told me that our neighborhood had an outage and explained trunks and nodes to me, I abandoned the cause.  The service returned Wednesday.  I have replaced our modem THREE times since we've moved just to be sure that's not the issue.  Our router is a year old; we lose signal on ethernet or wireless.  We switched the modem to a new sB 6183  that hooked up just fine but went out after about 15 minutes.  I called Cox and went down the reboot road once again.  No luck.  I gave up on this CSR when he started the standard "it must be your splitter" routine.  Third call resulted in a good connection for about an hour.  The third CSR told me the Cox system had flipped back to the old modem, that the setting hadn't been saved properly.  Service out again in about 15 minutes.  Fourth person went through the new modem activation very slowly and service returned until 6 pm tonight when I gave up.  It came back around 7. When this happens modem's power light is on and receive light is steady.  The send light flashes. 

WE ARE TWENTY YEAR CUSTOMERS!  All I want is a reliable internet connection!  I am paying for it but cannot control its consistency.  Here's my questions for the forum: (1)  I am going to have our contractor replace the coax from  the box on the outside of the house to the smart panel where there is a (Cox-installed) splitter.  We live with extreme sun; what is the best coax cable for this climate? (2) Can we run two lines from that box outside the house, (one for the internet and one for the TVs) or do the lines have to be split at the outside box?  (3) Should we put amplified splitters on the TV coax and/or internet coax?  We have 5 tvs, 3 computers, 4 ipads, Cox phone, cell phones, etc.  (4) Should we use 1 or more GHz coax for tv or internet? 

As you can tell I am no expert at this but apparently the people who have come by aren't either since we can't get steady service.