There is the chance that HMRC would see this as a joint business activity especially as you appear to still be active yourself in the business (ill be working the rest of the year for no extra money).
Your involvement in the business and the same activity in the same location with the same vendors or suppliers is too closely related.
For Ireland you would treat the rent like any other business income. I do not see how you can use this method to avoid VAT.
You could rent out the other but it is income to the business. If you had another entity that held the 2nd trailer and it was not part of your activity then that would be separate.
You would need to make sure the person you lease to is not already business related to you. VAT avoidance is is not over looked. Back in 2008 a case was ruled on between to partners and them trying to use a lease arrangement to avoid tax. They were in housing but the main point was the court saw their main purpose was to avoid VAT.
The VAT is on after threshold amounts.
If you register for VAT on the 1st of September, and operate returns on a bi monthly process (every two months), your first VAT3 will be for September/October, and will be due on the 19th of November.