There is nothing wrong with leaving the mosque after the adhaan to go and pray in another mosque

No File Exists
Check below answers in case you are looking for other related questions:
She relieved herself in a cup in the Haram
Ruling on women going to the masjid (mosque)

No File Exists
Related Answers:
What is the reason why the grave of the Prophet (peace and blessings of Allaah be upon him) was incorporated into the mosque?
Ruling on doing weddings in the mosque and always starting with recitation of Quraan and exhortation
Is it permissible to remove the innovators from the mosque?
She relieved herself in a cup in the Haram
Ruling on women going to the masjid (mosque)

Recommended answers for you:
The degrees and levels of Paradise and Hell, and the deeds that take one to them
What is the ruling on offering congratulations on Friday?
Repeatedly Committing a Sin and Repenting from it
Islamic actions for welcoming a new baby
Reading Soorat al-Mulk protects one from the torment of the grave