Is it permissible to pray without performing ghusl after light marital foreplay that does not go beyond kissing and touching, due to the unavailability of a bathroom at home and the difficulty of performing ghusl elsewhere?

If manī (seminal fluid) is discharged due to foreplay, ghusl (ritual bath) becomes obligatory before prayer. One should not delay ghusl except in a dire necessity, in which case tayammum (dry ablution) and prayer are required to observe the sanctity of time, and the prayer is to be repeated after performing ghusl, according to some scholars. However, if only madhī (prostatic fluid/pre-ejaculate) is discharged, then washing it off and performing wudūʾ (ablution) are required, but ghusl is not. A woman's manī is usually yellowish and thin, and it might be white. It is distinguished by a smell similar to a man's manī, or by the pleasure and culmination of desire that follows its discharge. If the manī is distinguished by color or smell, ghusl becomes obligatory. If it is not distinguishable between manī and madhī, it may be considered madhī, and only wudūʾ is required. This is the view of the Shāfiʿī school.