Don't get too serious in the first couple of meetings. Your boyfriend should talk to your kids as friends, taking interest in their lives, having fun with them and developing a good solid foundation. There should be no serious or future-related conversations in the beginning. Keep it light.
Reaffirm your Love for them
Kids often feel threatened by the presence of a new man. Not only does this man mean their dad is definitely not coming back, but it also means that they aren't the only ones in their mom's life anymore.
Children often feel neglected or replaced when their mother starts spending time with a significant other. Going out without them and showing love for someone else makes them feel like less of a priority in your life. Affirm your love for them while you're dating. Make sure they know you will always be there for them and that you do not love them any less just because you have a new man in your life.
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Stray from the PDA
PDA (public display of affection) is an outright threat to children. Until this point, your kids have only seen you kiss one man - their father. To see you kiss a new man whom they barely know is just going to confuse and frighten them.