(if this isn't allowed here, then the authority may delete it because I'm not sure if it's allowed)

If you know Button Mash, then you'll know his mother is an overprotective mom who will do anything to make sure her little babies are ok. It's even in her cutiemark!

So let's think for a second that Button's mom was the Princess of family. Cadence could still be the princess of love and Flurry Heart could be princess of whatever she was anyways. (Happiness I think)

Further into the topic, how do you think Love Tap would become a princess in the first place? Do you think she sacrificed herself to save her family from something, because that's something she'd probably do. Or maybe Celestia gave her a test and she passed it?

Just think about it.

how do you think Love Tap would become a princess in the first place?

Well, she's a fandom OC, so at least there is leeway for her personality and backstory. The first problem is that she doesn't seem to be born with a grand destiny, so whatever gives her princess powers would have to come from her and her alone.

The second problem is that princessly duties are, well, duties. Things are expected of a princess, especially an adult one. Becoming the Princess of Family would involve the same contradictions as becoming Princess of Friendship or Love: the title and its duties eat up into time spent on your own family, friendships, or love, or whatever.

I only really see one option, at first glance. A disaster happens, and it leaves a lot of children (say, six to a dozen or so) in need of a temporary home. Could be war orphans, changelings from a hive Thorax can't take in, baby dragons, whatever. Love Tap, given her talent, offers her services, her own family gets swept up in it but manages. Button Mash would then have to be (re-)written as a new big brother to all these kids, in particular organising the games to keep them distracted and happy. That kind of fits his cutie mark, still, to a degree.

Whatever disaster created this problem follows the children into Love Tap's home. If it's a plague, the infection reaches her. If it's a predator, it's tracked the scent of the little ones. She is faced with an ultimatum: turn her back on them or be destroyed along with them. It'd be easier for a predator: the set-up and temptation is pretty simple for that: "These are not her children, her husband and son are exhausted from taking on all this extra pressure. The natural state of affairs is for these little ones to die." Of course she doesn't take that, she instead lunges at the thing and brings some Earth pony might to bear. She gets knocked out, seemingly destroyed, and even Celestia is surprised to see her in limbo. Then cue the ascension, the glorious return, and some magical momma bear mauling. In the aftermath, the children in her care do get new homes, and life returns to normal, giving her the chance to actually be a mother to her family again. Until the next family-related disaster, of course.

So for it to work, you'd have to write a predator and prey into the worldbuilding, firstly. The predator has to be something intelligent and capable of reason, otherwise it can't offer the temptation. A good reference would be Nox in his first appearance, on Wakfu. His only goal was to suck out life energy and he was willing to do that to eggs, so... take note of that, if you can find it.

The prey, for maximum effect, should be something ponies are relatively unfamiliar with, but magical enough to warrant being predated upon. Best options there would be changelings or bat ponies. They would also need a reason why they can't be with their own kind, but there's options there too: a specific mutation that leaves them vulnerable to disease until a certain age, their innate magic being irritable towards their own kind, that sort of thing.