If these guys hadn't suggested 2 training sessions, then that's what I was going to say. I'd say this is a very powerlifting biased template, not sport. So as everybody has already said what I was going to, I'll do what they haven't and suggest a template to put it all together. This is how I'd maybe do it, not put too much thought into it, so maybe somebody elso could expand on it, or you could correct and finalise it yourself.
(Written as a training week from start to finish, not a calendar week)
SA - Speed / Strength work
SU - Rest
M - Strength work
TU - Rugby Training
W - Recovery work
TH - Rugby Training
F - Rest
It would look something like this;
Short sprints/jumps/ideally cleans or pulls depending on how technically sound you are (also work on your O-lifting technique as a warm up)
Squats - 90%, 2 reps x 4
Push Press - 3 reps x 4
Squats - 80-83%, 5 reps x 5
Bench Press - 80-83%, 5 reps x 5
Pull Ups - 4 x max
GHR's - 6 reps x 3
If you have access to a pool, get in it, and throw in some cold showers and static stretching. If you don't, lightly walk, cycle, row and throw in some bodyweight or very light exercises. Active recovery is better than complete rest.
My thinking behind this..... Speed, power and technique work always to be done first when most fresh. This is why you've got a day off on Friday, and this is the focus of your first training day after rugby training. As you want to gain strength as a main focus, you have some strength work at the end of the session. Rest on Sunday to recover. Monday you have your strength focused session. Endurance work (which is what I'll be taking your rugby sessions as) is always done last, thus after your strength work. Wednesday is to help you recover from Tuesday so that you're not too tired for Thursday's session, and getting more fatigued on top of already existing fatigue, as this will screw with your Saturday sessions. i don't think you need any HIIT training as you'll be getting specific conditioning from you training sessions
This may be a controversial opinion, but if you're not a starter, it may be an idea to sack off your Thursday session when game days have come, so that you don't have to drop a gym session, as otherwise you will probably be over-working your body. If not, you may have to drop to one heavy, and one light session, and this will obviously not build on your strength levels.
Just my views...