Surely H can see that an on-again, off-again relationship is not beneficial to S. Try to find a way to calmly and objectively communciate this with H. Maybe ask him how he would feel if you were to involve S in a relationship that has proven to be unstable.
If H is so sure that this is it and it will be long-term from here on out; then no harm in waiting a few more months before involving S, no?
