Advice about bonus sons mom not giving a sh*t

Advice needed.
Me and my partner have 3 kids between us a child each before getting together and a child we share. We have a lot of problems with my bonus sons mum (partners ex) she does not communicate with us about anything relevant, messages to tell the kid have a good first day at school but leaves it weeks before telling us about him being in a car accident. We have a 3 days one week and 4 days the next week cycle of keeping him. Both mum and dad work and always relied on my partner’s parents to care for the child. I’m a stay at home mum since expecting the son we share so I do the school pick ups for all the kids and my partner relies on me instead of his family now and they’ve pushed us away since I started helping out. Bonus kid is now being sent to an after schools club and being picked up by a grandparent instead of the mum. Eating with them and then mum picks him up just in time for bed, not spending any time with him throughout the week. This is resulting in homeworks not getting done, even before he started attending he told us he would like to come here instead and do his homework and then play with his friends I have no problem picking him up even when it’s not our days but mum has went a head and sent him to the club. Mum pays no attention to her son when she has him, his screen time is usually between 6-8 hours on the days she has him, treats him like a baby and does everything for him (he’s 7) he’s very independent in our home and we know he can take tantrums with her and we never experience anything like that when he’s with us. I’m usually the one who notices when the child has something coming up in school both parents don’t seem interested in his education. I feel like I’m picking up pieces for a bonus son when the mum herself would be bothered. We know we can’t control what the mum does when she has the child but sending him to these clubs before and after school resulting in roughly 8 hours of school a day and his homework not being done isn’t right on the child, she clearly has a problem with us having the extra time with him but it’s the child who suffers and I’m the only one who seems to care. What do I do, I feel hopeless. I’m not his parent I have no rights. We are taking records of things but going to court won’t do anything here as he’s not in danger but is being neglected in aspects of his life.