If you plan to take your family with you on a work trip, you can sometimes use frequent flyer miles or companion tickets to cover their travel expenses. Presumably your own ticket will be reimbursed, either by your employer or by a grant. Many credit cards link directly with specific airlines which can help you in two ways. First, you can accumulate miles through frequent flier programs and then use those miles to “buy” tickets for family members. Secondly, some credit cards offer companion tickets, which allow a second passenger to fly with a ticketed passenger for a nominal fee, as an annual membership benefit. Both of these options may have restrictions. However, conference locations and dates are typically known more than a year in advance. So if you plan ahead, using either of these options should not limit your travel flexibility.
If you decide to bring a child with you on a work trip, then you will need to have a plan for that child while you are working. Sometimes children, especially infants, are welcome to attend certain conference activities but sometimes they are not. Another option is to have a work colleague babysit for your child for a short time while you are getting settled on the plane, giving a presentation, or running a meeting. If none of those options is a possibility, then you will need to bring another adult with you.
Potential traveling companions include your partner, various family members, or friends. Invite different family members from your “village” to attend individual conferences and spend time with your child(ren) while you work. Maybe you and your child can have some quality family time with one of your siblings or other relatives. As payment for the babysitting, you can pay for or split the airline ticket with them. Alternatively, get your relatives to come and stay in your house with your child(ren) while you are away. If you can bring just your partner to the conference, then the two of you can go out to dinner three nights in a row which might be absolutely unheard of at home.