A few comments, first of all using the link() as @sanyaissues suggests is a perfectly valid solution, but in order to prepare for the second case I would like to also present another variant:
`= "[[" + this.mother + "]]" `
Here we build the full link within the inline query, and that works better than doing the brackets on the outside. A similar approach could be used to build the twitch link, if you do like the following:
`= "[" + this.twitch + "](https://twitch.tv/" + this.twitch + ")" `
Finally, since Obsidian now fully supports links in the frontmatter, you might want to consider changing the definition of mother into:
mother: "[[Jeanette Doe]]"
Which would allow for the simpler `this.mother` alternative in your text. This would also make that link appear in the backlinks pane, and be possible to rename, and do whatever you want to do with links…