Allah says (Quran, Ghafir 40:60) what translates as:
Call Me: I will respond to you.
This means that Allah will answer your dua. So if you have a need then ask it of Allah. If you need something for your children or you need help in raising your children then raise your hands and supplicate to Allah.
Here is a little story about a mother's dua for her son. Imam al-Bukhari's mother used to worship and make dua a lot. Allah honoured her and her son remarkably. Her son Muhammad [Bukhari] lost his eye sight when he was young and his mother saw Ibraheem al-Khaleel (the Prophet Ibraheem) in a dream and he said to her: "O you, indeed Allah has returned the eyesight of your son due to your supplicating a lot.’ In the morning Allah had returned his eyesight." [Collected in 'Sharh Usool Itiqaad Ahl ul Sunnah Laalka’aee 9/290] Translated by Abbas Abu Yahya.
I've been listening to Muhammad Alsharif's Visionnaire about making the Ultimate Dream Duas and there are two things that I've learnt that will 'raise your duas' and have them answered. These are:
Do It With Complete Faith
When you make dua, you have to believe that Allah will answer you. You have to have complete faith in this and not be doubtful.
It was narrated from Abu Hurayrah that the Messenger of Allah, peace be upon him, said: “(The Dua) of any one of you will be answered so long as he is not hasty in seeking a response and does not say, ‘I made Dua but I have not had a response.’” (Narrated by al-Bukhari, Muslim)
When you tell yourself or others that your dua isn't being answered then you do not have the belief that Allah will answer you. Have patience and a surety that it will.
Be in Gratitude
When you're grateful and give thanks to Allah for what He has already given you then Allah will give you more: "And [remember] when your Lord proclaimed, 'If you are grateful, I will surely increase you [in favor]; but if you deny, indeed, My punishment is severe.' " (Quran, Ibraheem 14:7)
There's always a good side to everything, just look at things positively. Thank Allah that you do have children - there are people who can't have any. Thank Allah that your children are healthy - there are some children that aren't. Thank Allah that, if your child has a disability, it has given you a chance to be patient and earn greater reward.
So turn to Allah for all the good that He has given you as well as turn to Allah when you need something.
PS Those on my subscription list will get this dua list template to help you to decide which dua to make for your children.