I do know that parents are like gods to their children. I have seen families where some worship God first then parents but also vice versa. Which one is the correct way?
The Scriptures,i believe, are indicating that parents should be worshiped before the Gods.
To prove this we can resort to the Pancha Maha Yajnas which are among the compulsory duties of every householder(Grihasta).
Every Scriptures,including the Manu Smriti, mention about these 5 great sacrifices :
The pañca-mahā yajñas are the daily duties to be performed by the householder for the rest of his life. They are the requiting of the spiritual debts (ṛṇas) occurred through taking birth on this planet:—
1. Pitṛ ṛṇa — pitṛ yajña = debt to the parents and ancestors, requited through honouring parents and performing their cremation and the memorial rites for them and the ancestors after death.
2. Deva-ṛṇa — deva-yajña = debt to the gods requited by performing the homa and other periodic ceremonies in their honour.
3. Ṛṣī-ṛṇa — brahma-yajña = debt to the sages requited through study and teaching.
4. Manuṣya-ṛṇa — manuṣya-yajña = debt to society requited through feeding of strangers and caring for their needs.
5. Bhūta-ṛṇa — bhūta-yajña = debt to the environment and other creatures by ensuring their food supply.
Now,from the order of the sacrifices one can see that the ancestors including the parents are to be satisfied first,then comes the Devas,Rishis and the rest.
Although this applies to the deceased parents but still it indicates that parents should come before the Devas or Gods when that order matters.
The importance of Pita(father) ,Mata(mother) and the Guru(tecaher,preceptor) are immense in the Sanatana Dharma.
For example,the Manu Smriti says:
2.227. That trouble (and pain) which the parents undergo on the birth of (their) children, cannot be compensated even in a hundred years.
2.228. Let him always do what is agreeable to those (two) and always (what may please) his teacher; when those three are pleased, he obtains all (those rewards
which) austerities (yield).
2.229. Obedience towards those three is declared to be the best (form of) austerity; let him not perform other meritorious acts without their permission.
2.230. For they are declared to be the three worlds, they the three (principal) orders, they the three Vedas, and they the three sacred fires
2.231. The father, forsooth, is stated to be the Garhapatya fire, the mother the Dakshinagni, but the teacher the Ahavaniya fire; this triad of fires is most venerable
2.234. All duties have been fulfilled by him who honours those three; but to him who honours them not, all rites remain fruitless.
2.237. By (honouring) these three all that ought to be done by man, is accomplished; that is clearly the highest duty, every other (act) is a subordinate duty.
The highlighted portion in the very last verse(2.237) clearly indicates that the worship of parents should precede that of Gods.
In fact,not only the parents,in all Hindu traditions, the Guru is also worshiped first before the Gods.