More ramblings as I think of them.
If she wants you to meet her parents/family after one date that could be a sign that she is a little too eager to catch a guy. Beware of these flags.
If the family is a little too readily agreeable to having their baby run away to American with you that could also be a sign that they are looking for a suppliment to the family income. Of course these are generalizations but you should still be aware of them.
Then again if she's just head over heels about you it's a good sign if she wants you to meet her parents/family/friends because she wants their approval. It is a major step up in her eyes if she is inviting you into her home.
Also keep in mind she may be hesitant to invite you home for any number of reasons:
1. Her sister (or even she) was involved with a gringo and he broke her heart.
2. Her father or brother(s) hate Americans.
3. She is very poor and embarrassed for you to see where she lives.
Of course none of these will matter if she truly loves you but give her time to deal with it. Colombians are very proud people and they don't like to look bad. They think all American men are wealthy and might look down on a poor girl from Colombia.
In my situation I didn't meet her parents until my 2nd trip to Cali. My girlfriend was somewhat embarrassed for me to see how she lived but it was something that had to be done. She wouldn't let me go anywhere except the living room on the first couple of visits.
When I first went to meet her family she already had the VISA paperwork I had sent to her. Her father would not let her send it back to me until he had a chance to meet me. Of course I told her that was fine.
Keep in mine I only spoke very basic Spanish and no one in her family except her spoke any English. I was sitting there with sweat rolling down my face while they 'chatted' with me with my girlfriend acting as translator.
But of course they liked me and by the end of the week I had their blessing to marry their daughter. They treat me like family and it's always a great feeling to be so warmly greeted each time I go for a visit.