M.P.
These are short term serious issues unrelated to everyday life. She doesn't know where she is or who you are in terms of routine. Adults have learned to adapt and have a mature brain. Her brain is literally making new connections and pruning out older connections everyday. Her brain is in the beginning of development and it takes energy to do this. Expect that she'll regress became of the stress.
Babies need routines You're traveling. She doesn't understand most of what's happening. She knows who you are but not why you're making her do things differently than at home. Home is the only place she recognizes. She's in a different space everyday. She's reacting to the unknown. Her comfortable routine is gone. She doesn't know what is happening next even tho she's with you. She's unsure about you. You're very different than you are at home. She is likely to be scared/anxious.
She doesn't want to be on the move again so she fights the car seat. You're right. She can't sleep because she's over stimulated and overly tired. Of course you don't want to miss anything in this country new to you. You're focused on what's happening around you. She feels that disconnect. She feels insecure. She's tired all the time. She's in a different time zone. Her body hasn't adjusted. She's anxious because nothing is the same.
I suggest you empathize with her. Allow more time to put her in her car seat and make transitions. Talk with her in a calm unhurried voice. Perhaps sing. Music is soothing.Sit next to her. Bring things from home with her to the car, her blanket. Give her, her lovey before going to the car. Talk in a relaxed and positive way about what is happening. Tell her you know she tired. Sympathize. Hold her while she cries. Physically forcing a baby and child rarely works when they become hysterical.
Off and on all day. Stop before she get's overly tired. Perhaps lay down with her when it's nap time. Just resting is OK. Focus on her with the goal of both of you relaxing. Hum, sing, play soothing music. Does she lay down in the same or similar space most days.
You're overly tired too. Make space for rest. Perhaps sit down with her and rest
every couple of hours. Talk to her along the way about what she's seeing. Call her by name. Wander away from the crowds once in awhile. Be aware of her feelings and empathize. All of this is hard to do when you're tired and want to see what is happening where you are. So cut yourself some slack. You need rest too. You are doing your best in a stressful and difficult situation.
Hopefully you have her in a pack. If she's in front where she can feel your touch, your heartbeat and hear your voice could help. Hopefully your husband will trade off with you.
Being in a new place, experiencing new things is stressful, even for adults. It's easy to forget the little ones also need more support than at home and difficult to focus on someone else's need when your body is tense.
Letting her cry for 3 hours damages her sense of security. Crying is her way to ask for help. I suggest she will continue refusing to get in seat. She now associates her seat with not getting help, with your tense frustration, with being scared/angry.
Perhaps practice getting in seat while car stays parked. Do not physically put her in seat. Talk calmly about how she must feel. Sympathize perhaps 5 minutes. Take her away from the car and play with her. Continue to do this until she is able to get in seat. Then gradually add more time as you take her to car