All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
First of all, we congratulate you for the favor of embracing Islam that Allaah conferred upon you, and we ask Him The Almighty to endow us and you with the grace of staying firm on it until death.
There are many ways by which you could be a good Muslim, and we have mentioned some of them in Fatwa 83931. So, please refer to it.
Prayer is one of the most important pillars of Islam, and it is an obligation to perform it on time. It is unlawful to perform it after its due time without a legitimate excuse. So, you have to try your best to combine between your work circumstances and performing the prayers on their due times. If it is necessary to combine Thuhr and ‘Asr, Maghrib and ‘Ishaa’, then there will be no harm in that, since it is permissible according to some scholars to combine those if there is a dire necessity for the person who will not make it a habit. The permissibility here is contingent on the presence of harm and difficulty.
It is narrated on the authority of Ibn ‘Abbaas that he said: “The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, combined both Thuhr and ‘Asr, and both Maghrib and ‘Ishaa' in Madeenah, when there was neither fear nor rain.” It was said to Ibn ‘Abbaas: “What did he intend by that?” He said: “He wished not to put his Ummah to difficulty.” [Muslim]
This is indeed one of the beautiful aspects of the Islamic religion. Thus, difficulty brings ease.
However, if it is impossible for you to remain in this work and avoid missing prayers, then you should leave it for another, given that Allaah The Almighty Says (what means): {And whoever fears Allaah - He will make for him a way out And will provide for him from where he does not expect.}[Quran 65:2-3] For further information, see Fatwa 82755.
As for your mother, you are obligated to be dutiful and kind to her, regardless of her disbelief, as shown in Fataawa 87019 and 90792. The best kindness you may do to her is to supplicate Allaah for her to be guided to the truth, and to invite her to Islam with wisdom and good instruction. The same applies to your sisters.
Furthermore, if your mother is poor, you are obligated to spend on her; and the same applies to your sisters if they are poor and are unable to earn their living. For further information, see Fatwa 85715.
As regards the fact that they are living in debauchery, then this does not exempt you, under Sharee‘ah, from being obligated to spend on them. But, at the same time, it is impermissible for you to spend on the one who likes to use what you spend on her to disobey Allaah, because Allaah The Almighty Says (what means): {but do not cooperate in sin and aggression.}[Quran 5:2]
Allaah Knows best.