There are many things that can make such a difference, Upgrading (Downgrading in my opinion) to the Jack may improve over all reception but it will not do much for your problem,, And it may in fact make it worse. Depending on the batwing model you have.
Very little beats the basic batwing.
Even less beats the batwing with wingman
Nothing on the market for RV use comes close to the batwing + Wingman + Sensar pro indoor module (This repalces your current wall plate with switch and LED, 12 volt and antenna).
Now to address your problem:
You say the TV near the wall plate works fine, but the other one 10 feet away (TV-2) not so well. Possibilities are:
1: Differences in the two TV. Some are better than others
2: Coax between back side of wall plate and TV-2.
2A: loose connection, at wall plate
2B: Loose connection at TV
2C: Bad coax
2D: Long path run of lowest bidder RG-59 (it may be 10 feet as you travel but what path did they run the wire? I have seen strange answers to that one and I'm not in the RV repair business).
3: Bad wall plate (replace with Sensar Pro)
My guess is one of the 2's however
Or there is a 2E.. Some idiot hooked TV 2 to the wrong jack on the back of that wall plate, The jacks, in order, with 12 volt at the top, looking left to right are
Antenna - Park cable - Tv 2 (Optional TV-3)
On the standard wall plate.. There are a couple of older models that are different however.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times