It would be nice if OP came back with some more info - age/grade of child, when the work was assigned, what the assignment actually involves, whether child was working on it between end of school Friday - 10am Saturday, etc.
Absent that info, some personal thoughts...
When my kids were younger - through middle school - they were on the way to Dad's in another state no later than the end of school on Friday, returning between 8 and 10pm Sunday. Dad felt that his time was HIS time, to have fun with his kids - not time for schoolwork. Okay. Not what I would have chosen, but I was also not keen on their being penalized for his choice. So I did a miraculous thing - spoke with their teachers, explained the situation, and asked if they could have an extra day to complete the assignments handed out on Friday. In almost every case, they were granted that extra time. Of course, I also impressed upon them that there was no reason they could not do homework while traveling, either by plane or car. Also that, if the assignment was given PRIOR to Friday, they should have it finished by Friday morning.
By the time they reached HS, I put the responsibility on THEM to figure out how to get it done. Whether they are with me OR with their Dad. They need to learn to prioritize their lives. And that sometimes means late nights. Or passing up something more fun to do. Or sucking up a poor grade for deciding not to do it/put in the effort. It's now on THEM. Just as it will be when they go off to college.
As for being home or not when they're picked up... All depends. I would normally be home, but there were times when I had to work. If they were old enough to be home on their own otherwise, there was/is no reason why they couldn't be when Dad came. If they weren't, then I'd have someone else stay with them. I don't see the issue, personally.
ETA... wrt the computer/access. When we do have a problem, like the printer's not working, access issues, etc - we contact the teacher. Printer issues are easily solved - jump drive, which is a good idea for the kid to use as back-up anyway. Of course, my daughter's school no longer allows jump drives to be used on their computers, so then one of us emails the work to the appropriate teacher to be printed at school. There are options.