Is what happened considered a tribulation from Allah that necessitates patience, or is separation obligatory, especially with the presence of a child and mutual love, after the spouses repented from following pornographic websites and speaking with strangers?

This tribulation is from Allah, and the couple must be patient, for tribulation is not necessarily a punishment for a sin. You both have done well by repenting, and you should increase in righteous deeds and purify yourselves. The husband must be a good role model and should not approve for others what he would not approve for his own family. He is not obliged to divorce his wife as long as she has repented and improved her conduct, especially since he loves her and has a child with her. He must commit to nurturing her and keep his home away from anything that could corrupt her.