Getting stuck when riding in a minecart or a pig.

I get stuck every time I ride in a minecart or when I ride a pig. I tried destroying the cart but only surrounding blocks and track are destroyed. A pig stopped the minecart and I was able to directly saddle and mount the pig but couldn't dismount the pig. Killing the pig was the only way to dismount it. I haven't found a horse yet to find out if the problem persists with it. As a matter of fact I haven't seen a horse or donkey after traveling a long way through forests, desert and through rainforest and swamp in peaceful mode. I haven't been brave enough to travel in easy mode or worse to find out if they only spawn in those modes.