Honestly, I can't see how you can effect them doing their homework and turning it in when they are only with you briefly each week. You'd really have to get in contact with the teachers and request homework for the weekends that you have them....at least you could supervise that.
What I had in mind was obtaining extra work specific to the subjects they are doing poorly in....math, reading, etc. You can purchase workbooks at teacher supply stores and make them do a few pages each day of the weekend BEFORE they are allowed to go to a practice or game. You may have to work with them to grasp the concepts (multiplication of fractions, whatever), but at least if they aren't doing their work at home....they are getting some exposure to the work with you and it could help their grades. You can find out from the teachers exactly what areas you could be targeting. You can also ask the teacher for practice worksheets after you explain what it is you have in mind. As a teacher, I would be glad to see a child's other family wanting to do something to try and help them. Also, there are numerous websites where you can print out math worksheets. I don't teach reading or Language Arts, so I'm not familiar with what's out there, but how about having the children read chapter books at their reading level and have to respond to you about what they've read???