Hello Yuri,
your understanding is correct
All STP
decisions are based on the following sequence of four conditions:
1. Lowest Root Bridge ID
2.Lowest Root Path Cost to Root Bridge
3.Lowest Sender Bridge ID
4.Lowest Sender Port ID
in your case the sender = root bridge and by lowering the STP port priority you change the 4 point in the list, the first 3 match.
If you change the STP port cost on the non-root switch port you are able to change point 2.
This is the more common way to influence the root port election and it can be done on a per vlan basis.
You can get some form of load balancing on two trunk links for different Vlans
Hope to help
Giuseppe