I would't swap the machines. Your cabinet is fabulous, and I would rather spend a bit of time and effort to get the Eldredge machine as rustfree as possible, oiled and polished. What brand and model is your daughter's shuttle machine? In my experience, it's better to get a cabinet that's made to fit the shuttle machine to beguin with. I don't know the Eldredge brand at all, but these cabinets had clever spring mechanisms, and very detailed and well made parts, don't muck them up!

I wouldn't ruin the cabinet by tearing it apart. It's an antique and probably worth money.

My second thought is you probably can't install a modern machine in that type of cabinet. Modern machines do not have places to screw them into a cabinet that drops down. I found this out when I bought a new machine and tried to install it in my old cabinet with the drop down mechanism.

They changed the cabinets to accomidate a lift system that raises the machine to sewing height. The machine flat on the base

Archangel2003's daghter's shuttle machine is probably an old one. An actual shuttle machine (as opposed to a round bobbin) was probably never made after the 50s. There proably are machine you easily could swap with the old Eldredge. A nice cabinet is not that difficult to come by, unless you want a very particular one. If the shuttle machine is a Singer 3/4 size machine, it is a bit harder to find threadle cabinets for it, than a full size machine, like a 201 or a 66.

If you clean and polish it up nicely it might get her interest in the old Eldredge. There are a few tricks to get these old machine super smooth; oil them with Triflow oil with teflon, or Finish Line Ceramic Wet Lube (Don't get too inventive with oils, some like 3in1, and others can cause trouble, pure acid free mineral oil is fine). They are finest quality oils, that will not gum up in any way (I promise), but the have teflon and (in case of Finish Line Ceramic), boron nitrate added, which does wonders for these old things. The lage gears on the threadle mechanism can take regular grease, but oil works too.

These threadle cabinets aren't worth a lot of money, but very nice ones fetch a bit. There are just too many of them, and not a lot of people use threadle machines anymore. They do change hands from time to time, and there is an interst in them as usable machines so not impossible to sell. It's really horrible to see any damage to fine cabinets like this though, especially for a purpose it might not even manage to provide.