How do I redo my floors?

Sand to bare wood, re-stain, then apply 4 coats of poly or similar, to seal the wood.

It is a messy messy process. I highly suggest relocating the pets during this process. It is not good for them to breathe in all that dust. Since you have hardwood all throughout your home, this is a major undertaking as you basically have to move out of your house, have the floors sanded, stained and sealed and that takes time. Then when cured, move all your stuff back in. You could do half your house, then the other half, but that may cost more. I would obtain several estimates before deciding.

https://www.consumer.ftc.gov/articles/0242-hiring-contractor

Throughout the house means that this a job worth bidding out to pros who have huge upright floor sanders.

I’ve done both: hands & knees with a belt sander & the pro approach.

You can remove the base shoe to save yourself some money.

I will be honest with you.....hardwood floors are NEVER pet friendly. If you want a pet friendly wood "look" floor, go with luxury vinyl plank flooring. It has the look of wood, but is made from vinyl and easy to clean. I have been in flooring for 25 years. The other option is plastic laminate flooring. Personally, the vinyl plank is much better looking and holds up well to cleaning! If you are dealing with REAL wood floors, you will have to have them rescreened every so often to get rid of the scratc hes.