I only have 4 kids though it feels like more lol😂 and our age spread isn’t as great but my oldest is 16 and youngest 8 and of course with a boy in the mix too we end up with many different interests. Firstly, I’ll just say it IS tough and a balancing act but CAN be done if all are willing to be reasonable and compromise. Children need gentle reminders that they are not the hub of the family but contributing spokes and the ‘wheel’ of the family will get thrown off centre if one person wants overrides everyone else’s. Sometimes having a quiet little chat to her as the ‘big girl’ in the family can yield surprising results. Your younger children have needs too although they may not articulate them in the same way.
Perhaps ask her does it have to be basketball? Could you search around for another activity that doesn’t require the same time commitment or has options for younger ones? Can you speak to the coach and ask if once or twice a week would be ok if she practices at home? Could you do your grocery shopping/library visits and other errands on basketball days?
Could one of those days be a catch up day with other friends ?
2 things we have done for activities and socialising.
Firstly we do most of our activities on 1 day a week. When my youngers having swimming, trampolining and gymnastics, I take my older daughter to her college course . There is a lot of driving around but it’s all one day. Then there was the need for socialising and there wasn’t a group that was available when we had time. So we started one our self. Yep, we started a mini co-op. It took a term to iron out the bumps but we do the things that are important to us. Nature study, music, foreign language, picture study and composer study. And a good bit of playing too! So the question is, Could you open up your home and invite a few over every week and have an informal coop/ play group? Can the mums share skills? It may take a while to get it to where you want it but you can do it and quite honestly most people are happy to have someone organise it. The energy it takes to implement would be far less than hours and hours in the car and you can still keep your baby in some kind of routine.
Just keep in mind, your child won’t die if you say No. Crying isn’t fatal either. Or whinging. Sometimes we just have to be loving but firm. Then get her to come up with some alternatives. Kids love a challenge.😉
Hope this helps in a small way.