With Respect To getting your necklace back, talk to a lawyer.

Assuming you are in the US, your state bar association will have a referral system. Check their website. The referral consultation will be low cost or free, depending on the state (and the attorney may charge less given you're a minor). If you are outside the US, your region's/country's/equivalent's professional attorney's association probably runs a similar referral service.

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Given that the necklace was a gift, you cannot claim it as stolen property. However, I believe that you are a minor. As such, you have some ability to back out of contracts and agreements, and those agreements and contracts can be cancelled by your parents. You may have a right to back out of this gift and demand it back; that will be state and circumstance dependent.

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(I hate the reddit fancy editor; any time i try to cut and paste, it deletes random sections of my drafts. Grrrr.)

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You may also have a claim under a theory of Fraud by False Pretenses. Your ex was materially enriched, and you were emotionally and materially harmed by your ex telling you things that he knew to be untrue. You may have a right to recover things you gave him that were premised upon you being in a real relationshop. Again, this will be state and circumstance dependent.

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Finally, assuming your ex is a minor, his mother may be wrong. She probably can (legally, if not morally) force your ex to give you the necklace back (depending on the custody agreement between your ex's parents). Certainly, if your ex's parents agree, they can force him to return it. If they don't, it will depend on the custody agreement and state law.

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It is entirely possible that you have no claim and are screwed. It is entirely possible that your claim to get it back is incredibly strong. No one on reddit who is qualified to make that judgement is going to respond to you in a public forum, as it could be professionally problematic. In the unlikely event someone qualified offers to you advise via messaging, it is going to be after a discussion about specifics, and they are going to need to know where you live (within state/city precision).

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In short, talk to a lawyer. Ask them if they think this is something that is worth bringing to small claims court, and what the process to do that will be. Also ask under what circumstances a custodial parent could force their child to return it, if a non-custodial parent could do the same thing, and if so, see if the attorney is willing to draft a letter to your ex's mother informing her of this.