No one can give a definite answer to this as it’s up to an individual immigration officer to decide.
You should be fine, but if questioned have the three proofs - 20,000 baht or equivalent in CASH, proof of accommodation for the first few nights and a valid ticket out of Thailand.
In Phuket you can use one of the three immigration offices. Phuket Town - most busiest, Patong Beach - not so busy or Blue Tree office - least busy. All have photocopy or photo places onsite or nearby.
You’ll need your passport, a copy of the passport photo page, a copy of your entry stamp in to Thailand, a passport sized photograph, a filed TM30 and fill out the forms TM7, STM2 and STM9. All forms are available onsite. Use a blue or black pen.
You shouldn’t have any issues travelling with both passports. If the check-in desk questions you ask for a supervisor who should know what they’re doing.