I have quite a few orthopedic issues, so I understand your concern. Believe me, I had my concerns!
You start out doing what you can do. For sprints, you don't have to run, just get your heart rate up. I have knee trouble, so it is impossible for me to go above 5 mph (currently, that used be be around 4 mph, but this diet really helped my inflammation issues). Do you have access to a Stair Master or an elliptical? You could use one of those for your HIITs, if you have joint issues. Find an activity you can 'go all out' on for 15 seconds, back off for 45 seconds recovery, then repeat. Work your way up to 8 repetitions first, though you may start out only being able to do a couple, and gradually increase your sprint time and decrease your recovery time.
As far as your LHT, have you tried the exercises in Primal Blueprint Fitness? Mark gives very good directions on how to gradually work your way up to doing the Essential Movement. Very good. I could not do a push up to save my life when I started, but I followed his instructions, and now I've worked myself up to the point that I can do 25 regular push ups per set, working on doing declined push ups. Once you can do Mark's 5 Essential Movements, you can work on doing weights if you want. I don't really want to do weights, personally, so I can't really tell you anything to try on that front, but I think the 5 EMs are an excellent starting point. If you can't do them, even with the modifications Mark suggests, maybe you can give us a detailed post about what the problems you're having are, and we can try to help, once we know the details?
Motherhood: When changing from pj pants to yoga pants qualifies as 'getting dressed'.