I can use both carts and also I logged out and back in and I still have both carts.
Also once I build my house walls one of my carts got stuck next to a wall and can't pick it up.
Hope this helps.
P.S. great job with the game though, really enjoyed playing.
I build one handcart.
Went and got some "Stone Block" empty it and then took it out to another stone deposit.
When I returned to my house the "old" cart was still there.
I added 6 stones in my handcart and once I used them my cart still had another 6 stones.
If I click the icon to see the contents of the cart with my character positioned next to it, then the cart is empty. If I move my character away and then check the cart contents the stones are shown.