Is it permissible to build a mosque with the money collected to buy an apartment in your home country, given the impossibility of buying the apartment except through usurious loans, or is that considered a dereliction of duty towards your young children?

You own your wealth, and your disposal of it is permissible. You may build a mosque with it or undertake any charitable work, and this is not considered a dereliction of your duty towards your children, as your obligation towards them is only their maintenance. If you save money for them to benefit them, it is better, based on the words of the Prophet, peace and blessings be upon him: "It is better for you to leave your heirs wealthy than to leave them poor, begging from people."