Blimey what a pasting. OP, I personally don't think that you're being that unreasonable.
I too have a sister who has kids, and who expects the family to take up the slack in terms of childcare, transport etc.
ie, bringing her kids to a restaurant then leaving them to run riot and expecting us to restrain them while she enjoys a pleasant drink etc.
I do not think for one minute that your DP should stay away in order to free up more room in 'the car' - assuming in fact that this is your car?
If it was AIBU they won't let me bring my DP to a funeral then we'd see another story on that one.
You just need to stop taking the responsibility here. If there isn't room for a car seat and your sister hasn't addressed this, then she won't be able to go anyway. Has she asked for your help in sorting this out? If not, then there isn't room and she will have to make her own arrangements.
If she's old enough to have a kid she's old enough to take responsibility for both the baby and herself.