I have small children and sometimes they cannot wait for me to come home from shul to make kiddush and then eat. Is it permitted to make kiddush and have the meal and davven maariv later on?
Please send sources.
Yes, it is permitted to make Kiddush before eating the meal.
In fact, several Rishonim (including the Raah (Berachos 27b) and the Ritva (Rosh Hashanah 9a)) write that the optimal way to accept tosefes shabbos is by making Kiddush (or alternatively by davening).
This clearly indicates that it is fine to make Kiddush and to eat the meal before davening. This is also ruled explicitly by the Magen Avraham (271:5).
The single source to my knowledge mentioning that this should not be done is the Maaseh Rav, citing from the Vilna Gaon (see no. 117). However, this ruling is not cited in other halachic texts, and many families with young children make Kiddush early in order to allow the children to participate, and daven later (or half-way through the meal).