2. Focus on New Friendship and Being Social
This is very important. You have to get out and meet new people. It may be difficult when you have softball games, PTA or custody schedules to adhere to. Don't sacrifice your alone time with your children for dating, but do find a way to slip in some "me" time. Get a hobby, join a meetup.com group or just get out and socialize with grown folks. There are various groups on Meetup.com dedicated to single gay parents so it's definitely a good way for you to meet people who share common interests and goals. It's guaranteed that you will make a few new friends.
Direct your focus on developing friendships over romantic relationships because you want to know as much info as possible about a person before introducing him into your kid's life. It will also allow you to share as much or as little of your story as you feel comfortable without feeling pressured by the idea of dating.
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Starting in a "friend zone" will help you determine if there is an existing foundation or potential for a romantic relationship to be built. It's much easier to transition from friends to lovers than it is from lovers to friends. Flirting With Strangers: 3 Ways To Break The Ice
3. Make Gradual Introductions
Take it slow when introductions start to come into play. When you decide to introduce a potential date to your children, introduce him as your friend. Depending on how open you are with your children, they may or may not get the idea of what kind of friend this person is to you. Regardless, you always want to use the term friend until it becomes a sure thing.
I would also advise that introductions be made while doing some sort of family activity together. Catch a movie, do a family game night and go bowling and invite your friend along. If he has kids, invite them along and make it a fun time.
I feel that this is important for a few reasons:
A) It's much easier to introduce your friend to your kids instead of introducing them to your boyfriend. Kids can get turned off and rebel against the term boyfriend if they are not ready or don't truly understand it.
B) It gives you the opportunity to see how your date interacts with your children and vice versa.
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C) It allows your kids to form their own opinions on whether or not they like your new friend in a neutral setting.