I would advise  to disregard this advice about booking.com. they do considerably better than Airbnb for me.

I will say that your LLC if it only has rentals should be a disregarded entity.

In most cases they are disregarded or are partnerships and that is typically, not a problem; however, it will lower basis.

When a judge determines that a defendant has established an LLC for legal protection and not for use in commerce, that judge may disregard the legal structure of the LLC and look through to its owners. 

Subsidiary LLCs will be disregarded that means the parent will file the tax return and regardless who collects the rent on behalf of the LLC it will record its own gross.No you do not have to pay yourself a salary from the partnership.

If the LLC does not file it's own tax return and all activities of the property will be reported on your personal Schedule E then that LLC is disregarded as a tax payer and the service will look to you and your wife as the taxpayer.  

Or report only under the parent LLC and don't report the child LLCs.I personally would report all the children and disregard the parent as the IRS prefers you to report each rental property separately.  

If they are rental properties that can be disregarded then yes.

Should I disregard their refusal and just install them?

The LLCs will be set up as disregarded entities.