The Bible is full of honest prayers. See Jesus at the Garden of Gethsemane. Or Moses at the burning bush. Or Paul in prison. Or Job in his struggles. God is not bothered by honesty. I believe He is bothered when we do not bring ALL to Him in prayer. It’s okay to question but don’t get stuck there. Allow God to do what He does best—work things for your good, if you belong to Him.
Be honest about your needs in your prayer time with your family. Don’t hesitate to ask your children to pray about certain issues. Of course, you don’t discuss anything they don’t need to know about. When they see you have prayer needs as well they will be more willing to open up in your prayer time. (Heb 13:18 )
No need to be stuffy or formal in your prayers. Kids might question your authenticity if you don’t pray to God like you speak in your everyday life. Remember, it’s a conversation, not a speech. If you are willing to pray instantly, your prayers will be authentic and come from the heart. Get in the habit of praying without ceasing.
Be quick to show answers to prayer too. And keep record of them. It will build your faith and bring more authenticity to your prayer time because you have specific praise to bring to Him and not vague “Thanks for this day” prayers.
You are an example. Model prayers that will last. Jesus did just that with the Lord’s Prayer (Matt 6:9-13) Allow the Holy Spirit to help you pray God’s will (Rom 8 ) and you will most definitely be authentic.