What's the tradition behind hand holding during the Our Father at Mass? In traveling around my diocese I've noticed that there are some parishes that are hand-holders and some parishes that are non-hand-holders and some people in the non-hand-holder parishes who persist in hand holding and some people in the hand holder parishes who abstain from hand holding. 

Also, there are some parishes where it is common to raise up your hands together for the doxology of the prayer. And some parishes where even unheld hands are held up like the priest does.

I know that pure imitation of the priest isn't good (his hands are blessed, mine aren't), but what I don't know is if spontaneous hand holding by the congregation is totally licit and where the tradition came from.  

My mom told me it was, "something Protestants did in the 60's that Catholic's picked up on" is that all it is?  Was there ever a Bishop who told his diocese to hold hands or not to hold hands?
It is not a prescribed part of the liturgy, and appears to be an accretion from Protestant tradition. One authoritative source says

To find the rubrics (regulations which govern the Mass) concerning these gestures, one may turn to the General Instruction of the Roman Missal (1970), On Holy Communion and the Worship of the Eucharistic Mystery Outside of Mass (1973), Instruction on the Worship of the Eucharistic Mystery (1980), and Instruction on Certain Norms Concerning the Worship of the Eucharistic Mystery (1980).
However, in all of the liturgical documents for the universal Church or of those particular ones issued by the United States Bishops Conference, no where is the holding of hands during the Lord's Prayer mandated. Frankly, this gesture arose among the various liturgical innovations in the aftermath of Vatican Council II.

He goes on to surmise (probably accurately)

Perhaps the holding of hands was introduced with good intentions to highlight the unity of the congregation as they pray, &quot;Our Father,&quot; not &quot;My Father.&quot;

As you say, there are those whose attitude towards the practice ranges from uneasiness to revulsion, and for those people the practice must be counter-productive!
That same commentator goes on to explain why it's not even necessary.

The unity that is sought really comes later and after a spiritual progression: First, we fall on our knees as the priest offers the sacrifice of the Mass: we recall not only our Lord's passion, death, and resurrection but also our need as individuals to offer ourselves to Him. Second, we pray in the words our Savior taught us, the Lord's Prayer, in which we ask, &quot;Forgive us our trespasses as we forgive those who trespass against us,&quot; even the person next to us in the pew. Third, we offer the Sign of Peace, a gesture found in the earliest Masses to show a genuine unity based on peace and forgiveness. Finally, we receive Holy Communion, which truly brings us into communion with our Lord and with each other. Looking at the logic of this spiritual progression to real unity, the holding of hands at the Our Father is extraneous.

At least one bishop is reported to have explicitly discouraged the practice:

WCPO reports that Bishop Foys [of Covington KY] wrote:

Special note should also be made concerning the gesture for the Our Father. Only the priest is given the instruction to &quot;extend&quot; his hands. Neither the deacon nor the lay faithful are instructed to do this. No gesture is prescribed for the lay faithful in the Roman Missal ; nor the General Instruction of the Roman Missal , therefore the extending or holding of hands by the faithful should not be performed.