I have three young children which consist of two girls and one very young boy. Our house is small so I can’t provide separate rooms for my boy and girls. My question is, is it permissible for my son to sleep in the same room as my daughters but in a different bed?
Alhamdulillah, all praise and gratitude we send to Allah SWT. Praise and salutations to our beloved Prophet Muhammad PBUH, his wives, family, companions and all those who follow his footsteps till the Day of Judgement.
Rasullullah PBUH said:
مُرُوا أَوْلَادَكُمْ بِالصَّلَاةِ وَهُمْ أَبْنَاءُ سَبْعِ سِنِينَ، وَاضْرِبُوهُمْ عَلَيْهَا، وَهُمْ أَبْنَاءُ عَشْرٍ وَفَرِّقُوا بَيْنَهُمْ فِي الْمَضَاجِعِ
“Command your children to observe prayer when they are seven years old, and beat them for [not observing] it when they are ten years old, and do not let [boys and girls] sleep together.” 
The majority of fuqaha are of the opinion that it is obligatory for a father or wali to separate the bedroom of his children between the male and female as well as children and parents. [See al-Mausu’ah al-Fiqhiyyah al-Kuwaitiyyah 38/34]
When commenting on the commandment “do not let [boys and girls] sleep together,” Ibn Ruslan said: “Between boys. And the separation between boys and girls is prioritized. The meaning of not sleeping together is to separate their mattresses between them.”  Badr al-Din al-‘Aini explained: “[The separation] of their sleeping place. The reason is when they reached 10 years old, they are approaching the minimum age of puberty and their penis starts to tense up. Hence, it is feared that something bad may happen.” 
Imam al-Subki said separating their sleeping place is by separating each child to one mattress or both on the same mattress but they are separated or not touching each other. If there are two rooms and one of the rooms is the room of the parents, then it is prioritized to prepare the room for the daughter. This is a precautionary step from any bad thing happening in the future.
I truly understand that in order to prepare a comfortable house depends on the ability of each individual. However, we advise parents to always follow the guidelines set by syarak in family management. If one isn’t able to prepare separate rooms, one should try to separate them even with a curtain or anything suitable. Allah SWT states:
فَاتَّقُوا اللَّهَ مَا اسْتَطَعْتُمْ
“So, fear Allah as much as you are able,”