Cycling to work and lower body strength training

[imambaccus]

I am going to start cycling to work, which will mean I will do about 10 miles each way (total of 20miles a day), I may have to cycle further 15-19 miles therefore 30-38 miles a day.

My current training program is as follows;
Mon- Martial Arts (just skill training, no cardio or resistance training)
Tues- lower body strength training (squats, deadlifts, lunges etc and flexibility express)
Wed- upper body strength training after work
Thurs-
Friday- 30-40 mins jog
Sat- lower body strength training (squats, deadlifts, lunges etc and flexibility express)
Sun-upper body strength training

As I do my strength training after work, will the cycling affect my lower body training? Would I need to rest for a few hours or so before I start or is the distance I’m commuting negligible? If it will affect my training, is there anyway I can work round it?

On a side note, I read Mr Kurz recent article on Bench press. I do incorporate these (dumbbell press) in my upper body workout. As I do all my strength training at home, what can I do as alternative to this, or is there no need for me to do them as someone doing a non grappling martial arts?

Thanks