Wa alaykum salaam, Maria,
InshaAllah, any rak’ahs (units of prayer) you’re going to perform after Isha prayer will count as qiyam (night prayer).
If you don’t think you can pray late at night due to your child’s situation, then pray two rak’ahs after Isha prayer, and then pray witr. This will count as qiyam for you.
Narrated Abdullah ibn Amr ibn al-‘As:
The Prophet (peace be upon him) said: If anyone prays at night reciting regularly ten verses, he will not be recorded among the negligent; if anyone prays at night and recites a hundred verses, he will be recorded among those who are obedient to Allah; and if anyone prays at night reciting one thousand verses, he will be recorded among those who receive huge rewards. [Sunan Abi Dawood]
So, again, if you pray two rak’ahs with 10 verses from the Qur’an, you will not be recorded among the negligent, and it will count as qiyam (night prayer).
Surat al-Fatiha is 7 verses. So, if you add another short surah from Juz ‘Amma (30th Juz of the Qur’an) you will satisfy the conditions of this hadith and fulfill a habit of regular night prayer.
If you want to follow the recommended way of praying shaf’ and witr, then scholars say you can do the following:
Pray 3 rak’ahs. In the first rak’ah, recite “Sabbih isma rabbika al-‘a’la” (“Glorify the name of your Lord, the Most High”) (Chapter 87). In the second one, recite a Surat Al Kaferoon (Chapter 109). In the third rak’ah, recite Surat al-Ikhlaas (Chapter 112).
Try to maintain this daily and you will get great rewards insha’Allah and will be counted among those who pray qiyam regularly.
If you feel you can add more, when your child sleeps, pray as you please in the last third of the night. Just don’t pray witr again (the singular prayer).
Also, make sure during this period–the last third of the night–that you make dua and ask for forgiveness. This is to correspond with the following hadith:
Abu Huraira reported Allah’s Messenger (peace be upon him) as saying:
Our Lord, the Blessed and the Exalted, descends every night to the lowest heaven when one-third of the latter part of the night is left and says: Who supplicates Me so that I may answer him? Who asks Me so that I may give to him? Who asks Me forgiveness so that I may forgive him? [Sahih Muslim]
And remember to renew your intentions while taking care of your child. Raising a firm believer is, in-and-of-itself, a huge act of worship. Ask Allah to reward you and count your raising of your child for His sake as an act of worship, and He will ease your affairs and put barakah in your time and in your child.
May Allah facilitate all of your affairs for you