that's wrong. they both do. you can't just cut out a major part of bitcoin network just like that.
miners provide the work which makes the difficulty go up and ensure the security and immutability of bitcoin blockchain due to expensive cost of 51% attacks thanks to their work. and nodes make sure miners stay in line by enforcing the consensus rules while keeping the network decentralized.

as for side-chain and mining, maybe it could happen alongside bitcoin in a similar fashion that merge mining works. the miner could be working on main net blocks with a much higher difficulty while finding hashes with a lower difficulty that could go into the side chain.