You're not unreasonable if you don't understand why the request was unreasonable, and it can be hard to understand if you don't have kids. I have three so I'll help you out here:
Babies who need support to sit can't be put in restaurant high chairs in my experience. These are made for children who can sit unassisted and don't offer support, they're more of a containment unit, like a dog leash, when you don't want your kid roaming free and tearing the place up. They're usually not allowed to go into this kind of highchair until they're 6+ months old. The big, bulky ones used at home do usually offer some support and can be used a bit earlier, but they take up as much room as a stroller.
It is also very difficult to do anything with an infant sitting on your lap, especially eating and drinking, because they grab at everything. It's like trying to eat a meal with a dog sitting on your lap trying to take a bite out of everything. They have zero table manners and grab everything. I say this an hour after spending three hours with my fourteen-month-old on my lap at a birthday party.
Strollers are essentially used in a similar way as a wheelchair and expecting a parent to move one is about the same as expecting someone who uses a wheelchair to remove themselves from the wheelchair and to sit in a regular chair so that you can take the wheelchair's space, this is why people are so grumpy with you.
Honestly, it's totally okay to ask, but you should approach it as if you're asking if it is hypothetically possible because you know it probably isn't. "I'm really sorry to bother you, but there aren't any seats anywhere. Do you think there's any way I might be able to schooch in somewhere with you and the baby? I'm not really sure there's a way I could fit, but I thought I'd ask just in case."
But getting take out is the best option in this situation. The baby was there first and you don't have any more right to expect the baby to move because it's in a stroller any more than you do someone who uses a wheelchair.