Increase Wifi Hot Spot Reception

In your case I think the better option would be a Wilson/Weboost Cell Amp. You can get a cradle that your hotspot can sit in for as little as $100 for a 3G version, which is all a light to medium usage person really need (similar to lower end DSL). The Wilson Sleek 3G will give you 25db, the 4G version will give you 23db (with the 10' antenna cable factored in). Even with their little stubby antenna if you get it up on the roof it will make a huge difference as the inside of your trailer likely will act as a Faraday cage.
The concern with your solution, is:
- the Hawking antenna is tuned for the 2.4ghz (wifi) it may but also may not work well on some of the cell bands. I have seen some antennas that claim huge gains in one band but have a loss in other bands. The Wilson Trucker antenna for the Wilson Cell amps is one that comes to mind. For some bands it comes in at +6db but for one of the Tmobile LTE bands it comes in at -2db and a hole lot of difference on other bands, where as their stubby that comes with the amps seems to claim about +2 to +3db on all cell bands/carriers (2G, 3G, 4G/LTE).
- I read a well written academic study done by an Electrical Engineer that basically said it would take heroic efforts to actually achieve 15db on a 2.4ghs Omni antenna. He concluded that almost every antenna he tested that was above 8db overstated their gain.
-assuming a 20' pole, with a total of 25' of cable. LMR100 will have a loss of about 12db (almost all the gain you would get from the antenna assuming their claim of 15db is accurate). LMR195 will cost you about 5db of loss, LMR240 will cost you about 3db of loss, and LMR400 will cost you about 2db. The last two are really not practical for home use and some connectors may not mate to them without a pigtail as well. Adding a pigtail will also cost you about 1db of loss as well.

I'm using Clear choice internet now which goes out of business Nov 5th.. Then I'll go with Sprint and the Zing modem with antenna ports. The Sprint Tower map shows a tower 9 miles from the Camp site which I think is pretty far but Their coverage map for Sprint Data /3g-4g shows that it has good reception at the Camp ground. The camp ground is heavily wooded along with each camp site(in the middle of a Forest Reserve). I checked the campground out yesterday it closed Sept 27th for the season but I walked back from the entrance to check out the sites. Next month When i switched to Sprint I can drive to the entrance with my Modem plugged into my Mini Van inverter and try it from the main entrance... but with all the tall trees back in the campground I'm guessing a outdoor antenna 20 -25ft up in the air maybe needed

It the Sprint tower is really "not far", you mak not need an antenna at all. Have you checked it?

From a little research and reviews I think I'll get the Hawking 15db Omni directional out door antenna It looks like it doesn't need weather proofing

http://www.amazon.com/gp/product/B000WEN7C2?keywords=outdoor%20wifi%20antenna%20hawking&qid=1443978850&ref_=sr_1_5&sr=8-5

No, a wifi booster will not help. What you need is something to boost the cell tower signal into your modem. That will need to be an external antenna like you have planned. You need to make sure your external antenna is optimized for whatever frequency band the tower uses.

Also.... will your external antenna need weather protection?