OP, if discussions are still ongoing with DC1 tomorrow I'd suggest you respond as follows (but in your own words).
"You are not speaking to the right parent about this issue.
If you want to look after your half sibling, then the conditions under which you are prepared to do that need to discussed with your father.
Be that the amount of time you're prepared to give or how you get to his house and back.
If he isn't prepared to meet those conditions you have a right to say no.
Just as I do and does your sibling, because it's not our responsibility to provide free childcare.
If your sibling doesn't want to do this then it's not your responsibility to lobby them into compliance on your father's behalf because you're unwilling to "do it all".
It's his responsibility to incentivise both of you into wanting to do this, either through providing transportation or paying for the service you're providing.
Even then it's still ok to say no. The same way I'm saying no, because childcare is the responsibility of the parents, not the elder children or ex partner.
I respect that your old enough to make your own decisions. You need to respect that your sibling and I can do the same and my decision is firm and final.
So if you want to move forward with this, speak to your father. Negotiate with him, the person who wants the favour and stop discussing it with me."