Advice on relocation from US with Dogs - Amazon Lux, UK, Spain, or Germany offices?

I’m a single 33yo female with 3* dogs. Initially from Russia, now a US citizen. I speak English fluently, Russian well, have conversational Spanish and am learning French. I’m open to learning a new language.

I’m considering some roles in EU but could use help deciding which city/country. The role is an engineering position with Amazon, options are Luxembourg, London, Barcelona, or Dortmund.

I’m seeing a lot of posts about how difficult it is finding a place to live with one dog, let alone 3. Would any of these cities be easier?

Dogs are all doodles in the 25-35lb range, microchipped, neutered, and up to date on all vaccines.

Considering current political climate in US, is one country better for getting residency? What are the cost of living and culture differences?

Any advice appreciated!