Hi Joshua,
I don’t know what type of grow light you are using but blue spectrum light will produce more compact plants whereas red spectrum increases joint length and induces flowering/fruiting (just think of the difference between spring and autumn sunlight).
Plants grown under artificial light will need to adapt to natural daylight and the leaves will scorch if they aren’t hardened off, by standing them out in a sheltered spot during the day for a week before planting them out.
If they are falling over in the trays it could be damping off, try to improve the airflow, reduce the heat a bit, and water with 1 tsp bicarbonate of soda in a pint of water.
Regards,
Tristan