JMHO

as jake was the first dog, he should stay, you could work on the dominance issues with max and jake. i think it would be unfair to re-home poor jake at this point in his life. as he has been with you for 7 years and know you as his only family.

also you could help to rehome "lady" into a suitable home where she will be well cared for, or even try fostering her for a while to see how things go.