You should probably add static stretching before you lift until you've adequately addressed your flexibility issues. If you're worried about the negative effects of static stretching pre-workout, make sure you do dynamic stretches and a lot of warm-up sets after the static stretching.
Yoga can be a good or bad thing, depending on how you do it. Yoga has you stretch in a general manner, which allows you to compensate for tight muscles. Essentially, you can have a case where tight muscles stay tight and loose muscles get looser.
If you know what you're doing, I think yoga can be great. It can be a fun activity and a good form of mobility work.