To do a cutscene-conversation-cutscene, just start the conversation with a blank node, and attach the first cutscene to that. Then have your conversation, then at the end another blank node with the final cutscene attached.
If for some reason it has to be done with scripting, the script to start a cutscene is CS_LoadCutscene. The cutscene resource is whatever cutscene you want to run. If you attach the script gen00cs_cutscene_end to the cutscene (which I think it does automatically), you can specify a plot and a flag in the function as well. That plot flag will be set when the cutscene is over. Within the action script for that plot flag, you can do whatever you want, including using UT_Talk() to start another conversation. If all you want to do is make someone start a conversation, you can leave the plot flag field blank, and put the tag of the speaker as the final parameter for the function.