Anything to do or see in between Carlsbad NM and San Antonio TX

***Disclaimer:  Our daughter has lived in Phoenix for 10 years so we have made the trip from Fort Worth to Phoenix at least 8 times by car.  We love to stop at interesting places, plus we did several of these attractions as individual trips while she was growing up.  Some of them are places we want to visit but have not quite gotten to .  
Be sure you have a National Parks Family Pass; with four people in the party you should save some money.  
First of all, it depends on the route you are planning to take; if you are driving  I25  from Albuquerque or Santa Fe (New Mexico)down to Carlsbad Caverns National Park Headquarters, go down to Las Cruces and take US70 east to White Sands which is a gypsum sand desert (if you have a National Parks pass, you can use it here).  Apply sunblock liberally and invest in some really dark sunglasses and good sunhats.  Alamogordowould be a good meal stop, then take NM82 to Cloudcroft About 18 miles  south of Cloudcroft, is the National Solar Observatory.  Continue east on NM82 (it is a lovely drive) to Artesia (New Mexico)where you can pick up US285 to Carlsbad (New Mexico).  (it is about 3 hours total from Carlsbad to Alamagordo) The park is a few miles south west; park headquarters is in Whites City.  After visiting the park, you can take a side trip SW to Guadalupe Mountains National Park  From the Guads, head down to Van Hornto pick up I-10.  Continue east on I-10; just past the I-10/I-20 split,  you will see signs for Balmorhea State Park, featuring the world's largest spring fed swimming pool.  There are cabins there, and the town of Balmorhea is large enough to have plenty of hotels.  From there to San Antonio there isn't much to do.This is one long drive featuring miles and miles of nothing but miles and miles.  Great for night sky viewing and amazing sunsets though!   Fort Stockton has a preserved fort and other historic sites, and is a good overnight choice.  Between Fort Stockton and San Antonio do plan to stop at Caverns of Sonora, which is one of the most beautiful and most photographed caves in the world; it is filled with pink gypsum formations which look like glass.  It's a small cave so the tours are short; make time to see it, if you can. Once you get to San Antonio, enjoy the San Antonio River Walk, San Antonio Zooand of course The Alamo. San Antonio has a nice bus run which starts Alamo Plazaand circulates around several attractions.  
If you have time! Head northeast from San Antonioon I-35 to New Braunfels for a day of recreation on the Guadalupe River. You can rent giant inner tubes and float the river. OR you can go to Schlitterbahn Waterpark, one of the oldest and largest waterparks in the US and spend the day there.  
Now, if you are taking I-40 from Grand Canyon National Parkeast to I-37 down through Lubbock to enter Carlsbad Caverns National Park Headquarters from the east, be sure and make some time to visit the Palo Duro Canyon near Amarillo.  If you are staying in Amarillo, get tickets for TEXAS! a musical production staged in the canyon.  
If you do this, when you cross I-20 on your way to I-10, you will be in the Midland-Odessa area. (location of Friday Night Lights)  West of Odessa is Monahans Sandhills State Park. You can rent saucer sleds and ride down the sandhills.  Texas highway 18 will take you from Monahans straight down to Ft Stockton.  
This is a lot of information, I know but this is a particularly attraction dense area because much of the land isn't good for much else except its beauty and uniqueness.  What are you doing between point of origin and Carlsbad? If you are coming through Las Vegas, just head down to Grand Canyon National Park, spend the night in Flagstaff, head south to Phoenix where you can pick up I-10 to Las Cruces, then over to Carlsbad Caverns National Park Headquarters.  Interesting things to do between Grand Canyon and Las Cruces are: Sedona, Jerome (Arizona), Saguaro National Parknear Tucsonor Kartchner Caverns State Park east of Tucson.  Kartchner has only been open a few years; consideration of the ecology and environment of the cave were the prime considerations in the development so it is unique among tourist caves in the US.  Jerome (Arizona)is an old copper mining town which is  well preserved with lots of cute little shops and eateries. It is very walkable.  If you stop there do not miss the Kaleidescope store.  Nearby are two national monuments:  Montezuma's Castle Visitor's Centerand Tuzigoot National Monument, both of which feature ancient dwellings.  
I'm assuming you will follow I-10 all the way across the rest of the trip until you get to the turnoff for Orlando.  Try to find time for a visit to the NASA Johnson Space Center if possible.  Allow at least 4 hours.  The beaches along the Florida Panhandle are among the finest in the world if you want beach fun.  
You may have noticed that you can spend two or three weeks in Texasalone.  You may find that Grand Canyon National Park would be a better trip on its own combined with the Utah National Parkswhich cover most of the southeastern quadrant of Utah
For handy reference material on traveling through Texas go here   https://www.traveltexas.com/travel-guide and order The Guide.  It has every little thing you might ever want to visit in The Great State of Texas, no matter how small.  And a map.  We get a new one about every 3 years.  You can also pick one up when you cross into Texas from any of the surrounding states, at the Welcome Center, but it is nice to have it in advance.  
Have a wonderful time.  Remember this:  when traveling across West Texas, it is wise to top off your tank whenever you stop for anything.  There are some pretty desolate areas out there where no gas stations exist.