You or your ex-boyfriend Jonathon can file a Petition to Establish Paternity and in the Petition you can request the DNA test.You or Jonathon may want to consider consulting with an attorney because of the time that has elapsed since Timmy has had custody for 2 years as you stated in your question. There is a possibility that Timmy's defense could be that Jonathon has abandoned the child, but the attorney should be able to advise on the issue and should know the "ins and outs" of the Court system and procedures.
As far as Timmy denying visitation, you can file a Motion for Contempt due to Timmy not abiding by the Order and request make-up visitation and/or additional visitation in the future. I believe we have already discussed this but please let me know if you have any additional questions.
If I have answered your question, please Accept my answer. Thank you and Good Luck to you!
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