Do you have what's often called a "mouse hole" where you push the cord into? If so, it sounds like the PO disconnected the 30 amp cord just inside the mouse hole and reconnected a 15 amp extension cord. No problem with that electrically, but yes, not good for running an AC plus other loads.
Sounds like all you need to do is buy a 30 amp (#10 awg) RV shore power cord and and reconnect to the trailer's wiring. You should have #10 romex cable at the mouse hole running to the 120 volt 30 amp panel that you'd splice to. If the PO changed that, you'd need to install some new #10 romex to the panel.
Some RVs have a detachable cord with twist-lock connecter on it instead, but I'm guessing you have a mouse hole setup.
The new cord could be a replacement cord without female connector on it like in 1st photo, or a 30 amp extension cord like 2nd photo and you'd simply cut the female connector off. Just need to make sure it's for an RV with a NEMA TT-30P plug. Available on Amazon, ebay and RV parts vendors for around $50. Or try your local Craiglist for a deal on one.
If you're somewhere that only has a 15 or 20 amp receptacle (typically at a home), you can use a 30 to 15 amp adapter as shown below which works fine for keeping a fridge and converter going.

