Sorry you are facing such a tough situation. A schedule is probably the most effective tool. That combined with doing as much prep (meals, clothes, etc) ahead of times can help. My husband isn't traveling but he often works unreliable/long hours so it's easier for me to take the lead. Here are some things I do to make life easier that save a few minutes each day and when added up could free up an hour or two.

Plan ahead meals- just having a plan on what you will cook for dinner helps reduce stress and time. I like to use the cheap/disposable casserole pans and put the ingredients and recipe for each meal in one. That way it's all ready to go and I can just grab the pan and get started. I haven't mastered cooking on the weekends for the week but I hear that helps. I also keep quick meals on hand for nights I am to busy/stressed/tired to cook such as the frozen skillet bags, pizzas, nacho ingredients (pre-made shredded chicken & toppings), etc. In the evening I get my lunch ready for work the next day and decide what will be for breakfast. For example if I am making a protein shake I get the blender out and put the protein powder near it so it's ready to go. If the kids are having granola bars for breakfast I get them out and put them on the table.

Have the kids help when possible- my oldest is 6 and she can get her back pack ready, clear the table and get sippy cups & snacks for her younger sister if I am occupied doing something else.

Plan ahead clothes for the week- yours are probably picking out their own but on Sunday I pick out clothes for the week for me and the kids.

Putting backpacks, stuff you need to take in the car with you for sports in the night before can help too.

Multi task when possible- here's what I do or have done
return emails from your phone while nursing/rocking baby to sleep
clean the bathroom (wipe things down & sweep) while kids are in the bath
Make a daily cleaning list of things you can do in 30 minutes or less and do a little housework each day rather than trying to do a big cleaning on the weekend. Here's an example:
http://www.realsimple.com/home-organizing/cleaning/daily-cleaning-checklist

Experiment until you find what works. I used to give my girls separate baths then try to put my girls to bed at the same time and I would end up a stressed out mess because both wanted my attention and it would take over an hour for them to go to sleep. Now they take a bath together which they love, then the oldest either plays with daddy or gets to watch a little TV while I get the baby to sleep. Once baby is asleep the oldest and I have story time together and then she goes to bed. Both fall asleep in 10-15 minutes now and it's much more pleasant.

As far as working out try to find things to do together or do it when they are sleeping. You can go for walks after dinner, turn on music and dance and play, play soccer or baseball in the yard, etc.

Take advantage of the childcare you do have (school). My oldest has after school care until 6:30 pm and the youngest goes to a daycare that is open until 6:30 also. I used to leave work at 5 then pick them up right away and try to cook and do everything while they were running around me in the kitchen trying to show me stuff from school or ask for snacks. Now I run home first (both daycare and school are close to home), change clothes, start dinner, and do a quick 15 minute clean up before picking up the kids. Now when they get home dinner is ready and they have my full attention.

Last don't wear yourself out. If dishes go undone one day or you give the kids McDonald's because you're too tired it's okay.

It is challenging. If you can't do typical exercise like running or biking try to find ways to incorporate more movement into your day. Parking further away at the store, taking stairs, doing squats while you cook. etc. Don't give up :>

Would it be possible to do videos? There are a ton on YouTube. We have a SmartTV so I can go right on YouTube from there. You can do them anytime, which is nice since it's getting dark too early to be doing outside workouts right now and I don't really have time for the gym. My son is almost 10 months old, and I can put him in the pack and play or exersaucer to occupy himself long enough for me to do a video or two.