Is it permissible for me to bequeath the retention of real estate and the distribution of its rental income to my children (two sons and two daughters), and should the male's share be double the female's share in this distribution?

If you wish to endow your real estate for your children after your death, an endowment conditioned upon death is valid and is considered a bequest within the limits of one-third of what you leave behind, with the remainder being inheritance. If the endowment is for some heirs to the exclusion of others, it is not valid, due to the Prophet's (peace be upon him) saying: "No bequest for an heir." If the endowment is valid, its distribution shall be according to what the endower stipulates.