You say you have an injury but ask any good personal trainer or strength and conditioning coach and they will easily find some forms of exercises you can perform by working around the injured part of your body. A physiotherapist or exercise physiologist can also use that time to help you recover from your injuries and it is during those times of rehabilitation that you can concentrate on correcting potential contributing factors to your injury, such as poor core activation, poor posture, incorrect lifting technique or biomechanics and overall cardiovascular and muscular fitness. That way you will come out stronger. I look after many athletes with chronic or long term disabilities and it amazes me that often they are more enthusiastic with exercise than many of us able bodied couch potatoes.
I remember carrying my 14 month old in a second hand baby backpack (it cost $20 from a church fete and was much lighter and more comfortable than the big expensive ones out there on the market!) and walking with him everyday whilst holding leads for 2 dogs. You'll be surprised how much of a workout you can get with that extra load walking up Mt Ainslie, or mowing the lawn or working out what is and isn't possible in terms of martial arts training and weights training with an extra person on your back. I see so many parents with jogging prams and baby carriers on bikes and sharing these times with your kids is so important for their development. Primitive man would have swaddled their kids on their backs when they worked as gatherers and farmers. Our bodies are meant to move and having kids with us shouldn't stop that.