I am pursuing a Master's Degree via distance learning (MA-MFT) to become licensed (LMFT). I'm interested in knowing if anyone is aware of any institutions that offer this program with anything LESS than 4 one-week intensives on site. I am interested in Christian Universities and am favoring Liberty University out of VA right now - but I'm open researching other schools.

You don't need to seek a school that specifically offers a degree in MFT; the key is, know the requirements for the LMFT in the state(s) where you're seeking licensure and make sure you get the coursework and practica you need to meet those requirements. You can get an MA/MS in counseling, social work, or clinical psych and meet the MFT requirements via electives and making sure you have enough hours in your practica (and the right practica).

My MA in clinical psych is from a brick-and-mortar school, so I'm not familiar with online programs. If by intensives you mean on-site education, my guess is that these are required for the faculty to evaluate your suitability as a candidate. It's difficult to impossible to adequately evaluate nonverbal communication via email or the phone, so I would expect some face-to-face contact being required. I see you have small children: maybe for the intensives, you could get a family member or church member to accompany you to help with the children?

Here's a list of online Masters degrees in counseling. You also might contact the American Association of Christian Counselors to see if they have any recommendations.