Is moving my hamster between two homes weekly too stressful for him?

This could be stressful to some pets, depending on their personality. I would suspect a prey-species such as a hamster would be more affected by the constant movement/change of scenery just because they may be more alert/aware of their surroundings. Whatever pet you decide to get, you will need an appropriate travel carrier to be sure the pet doesn't get loose in your car. Or even better, if your car is large enough to move the cage between the two households this may be easier on your pets so that the actual cage itself isn't changing regularly. Covering the cage with a dark sheet can be calming for some pets during travel, so they aren't alarmed by the light/noise on the trip.

Many of our exotic companion mammals, such as hamsters, will do well in the car if their environment is kept stable. Since you are taking her in her cage, that may help. Other things that you will want to do is remove the water bottle while you are actively driving, but if you stop to take a break (ex: for gas, for you to eat something, or to use the bathroom), make sure that you put the water bottle in to give Mamy an opportunity to drink. Ensure that she has food available at all times as well. I would also recommend removing her wheel while you are actively driving so that she doesn't hurt herself on it. One of the most important things for you to do in the car is to make sure it does not get too hot or too cold. I would recommend running the air conditioner in your car to get it to the temperature that your house would typically be, but make sure that the vents are not blowing directly on Mamy. With Mamy being a hamster, hopefully she will sleep the majority of your time on your drive (unless you plan on driving at night). If you notice that she is restless or seems stressed, then I would recommend evaluating the temperature first. This is often the most stressful part of traveling for these little guys. If you plan on staying in a hotel (which for that long of a drive it may be a good idea, just to give her a break), then you can have her cage set up as you normally would during that time. I hope that helps, and that your trip is a success!

This is a great question, and I am very glad that you are thinking about this! To help to keep Gus cool during this time, you can utilize ice packs around the carrier or cage while the A/C is turned off. If you plan to utilize these, I would recommend ensuring that Gus does not come into direct contact with the ice packs, as he may try to eat them, or may get too close and get "burned" by the more extreme cold. I hope that gives you a place to start, and good luck with your move!

It really depends on how old Frankie's babies are, if they are still curled up in the best I would try your best not to disturb them. However if they are older and exploring about as long as you are gentle and don't leave any separated for too long you can move them fine.

No, I would not be overly worried. He may just be tired from stress. Just keep an eye on him and if he isn't better in 24 hours you should take him to a vet for an exam. He may be coming down with an illness; very common, especially if purchased at a pet store.

I think you need to give him more time to calm down. One day is not enough. If he is very stressed it is best to cover the cage for a few days and bother him as minimally as possible. This will give him time to acclimate. This linked article below may help you more. https://hamsters101.com/help-hamster-adjust-new-home/

He will likely be fine. My only concern is that that stress him and he may develop an infection later. Watch him to make sure he is eating and acting normal. If not, I would have a vet take a look at him. You may have to have a health certificate to fly with him so be sure to contact the airlines to see what type of paperwork you need.