When you purchase with Swan, the purchased amount goes into a custodial account, where they hold it for a period of time, no longer than 30 days, before you can withdraw it to your own wallet. This is to protect them against fraud, and is perfectly acceptable.
The custodian of the bitcoin is Prime Trust, the same custodian that Strike and 700+ others use. They're one of the most trustworthy in the space, imo.
Once the locking period expires you can withdraw the BTC to your own on-chain wallet. They do not (yet) offer Lightning withdrawals. The process to withdraw is straightforward enough, but involves you having to click a link in a confirmation email. Straightforward for us, but you may want to hold your mama's hand as she does her first, or offer to do it for her.