Coffeemaker

Assuming you do not own the repeater, you should ask the repeater owner if the system is capable of multiple PL groups.  That type of setup was commonly used back in the day for Community repeaters, where each user group (plumber, HVAC, Landscaper, etc.) had their own PL tone, but they all shared a common frequency, and each user had to monitor to make sure that the repeater was not in use by one of the other groups before they would Key up on their PL.
If the repeater has Multiple group capability (Every Kenwood TKR-850/851 came with that feature right out of the box) then it's simple to just request your own separate PL tone for your group.  Expect to pay for that feature if it's available.  Listening to a repeater's output in Carrier Squelch would defeat the purpose of having a separate PL tone. Set up properly, your daughter would only hear you when you keyed up using the special PL tone. Other traffic on the repeater would be nothing but a flashing receive light on her radio.
It's 1970's technology, so don't expect any actual privacy or miracles - but it would do what you're asking for.

While you can't talk over another user, should the repeater not have a PL tone, you might use your own PL tone to reduce the chatter each of you hear from the repeater.  My radios will show a signal on the frequency even if it has a different (or no) PL tone from the one you use. 
Can you put up a tower or some sort of elevated high gain antenna at one home and avoid the repeater?

Ha! Did you just link to this same thread? 

TippCity625 is a good repeater without much traffic.  I have been able to hit it as far south as I-75 and Needmore Rd with a 5 watt HT.  Seems like the operator told me the antenna was on a silo, so it's not really tall.  That makes it susceptible to the small hills in the area. 

Increasing 5 watts to 10 watts is +3 dB.  Is that worth it? 

Even if it is, it is a worthwhile investment to keep the whole world at arm's length. 

You won't transmit very far, but until the output stage/output transistors overheat, it shouldn't hurt a thing.  With old tube gear and maybe output transformers, I have no idea. 

I have enjoyed my Wouxun (ocean) 805 and 905 handhelds.  Both can use repeaters and have excellent power output.  The 805s are easier to program, but their filters are weak, meaning high power repeaters will bleed over into nearby frequencies.  I have had staticy conversations over a repeater 110 miles away, mountain to mountain, using its rubber antenna.  The 905 is a better radio with longer battery life and better filters.  It's software is a little more difficult, but not hard to use.  It has also linked to that repeater 110 miles away both with its rubber antenna and a roof mounted antenna.  A good roof mounted antenna will allow your handhelds to do everything a higher powered mobile will do, except maybe power through a stand of trees. 

I spent several minutes with the search function.
What is a "net" and what is its purpose?  I have listened to a few minutes of net conversations and can see no point, other than proving one's radio works and perhaps that the links work.  It doesn't take 100 people from 3 states to prove the system. 

I'm at 2350 and both repeaters are about 3300 feet. 
I've used each repeater with an 805 and a 905.  Mostly the 805. 

My 5 to 5.5 watt Wouxun (ocean) handheld can carry on a conversation with an Atlanta area repeater 110 miles away, with a little static.  It can hit an East Tn repeater 72 miles away clearly.  Other than a few dozen trees around me on my mountain property, both are unobstructed line of sight transmissions.  With UHF it isn't all about power. 

My 5 to 5.5 watt Wouxun (ocean) handheld can carry on a conversation with an Atlanta area repeater 110 miles away, with a little static.  It can hit an East Tn repeater 72 miles away clearly.  Other than a few dozen trees around me on my mountain property, both are unobstructed line of sight transmissions.  With UHF it isn't all about power. 

My 5 to 5.5 watt Wouxun (ocean) handheld can carry on a conversation with an Atlanta area repeater 110 miles away, with a little static.  It can hit an East Tn repeater 72 miles away clearly.  Other than a few dozen trees around me on my mountain property, both are unobstructed line of sight transmissions.  With UHF it isn't all about power. 

My 5 to 5.5 watt Wouxun (ocean) handheld can carry on a conversation with an Atlanta area repeater 110 miles away, with a little static.  It can hit an East Tn repeater 72 miles away clearly.  Other than a few dozen trees around me on my mountain property, both are unobstructed line of sight transmissions.  With UHF it isn't all about power. 

I had to go into Windoz settings and force the com port to port 1, I believe, to get the software to recognize the 905G. 

We are peripheral to any IMS/ICS.  They find and forward us work.  I regularly call the local Emerg Mgt Agency for updates and info on the areas needing help.  So, the answer is a little of both.  We partner with a local church and send out volunteer work crews from the church.  We provide the volunteers with tools, meals, showers, laundry and sleeping quarters at/in the church.  We almost have the capability to setup in a parking lot and run alone, but that's not the best way to do it.  As we are not officially part of the ICS, we don't get their comms.  Plus, what we need is our own link to our work crews and our base and between "Black Shirts". 

All true, but we don't work in Chattanooga often (once).  We need communication from our work base to several work crews in the field and from coordinator to coordinator.  Sites are most often some random town in TX, LA, or FL.  We'd have to have an amateur operator sitting/working with each crew and at the work base.   Once the cell systems are repaired, phones work better, but until then, we'd like to be self sufficient.
 
As for height, I may be able to put the antenna on a nearby building, but we will always have the tool trailer when a big disaster happens.