There is no RAW way to combine Sneak Attack with Unarmed Strikes
In order to allow this, you'd need to either waive the Sneak Attack requirement for a Finesse weapon, or create a homebrew item that work as a finesse weapon but still an unarmed strike.
Even Unearthed Arcana has the major warning that it is not tuned for multiclassing, but once you start multiclassing with UA or Homebrew, you enter unprepared territory. It's up to the DM and they're table to decide how they want things to work. Allowing certain interactions (i.e. if the spiked glove is considered a finesse weapon), may break certain other things (i.e. rogue sneak attack.) There are generally trade-offs for making decisions and if those tradeoffs disappear because of homebrew, then you may end up with a character who is more powerful than they should be.
The dangers of allowing this interaction
But in the end, it's up to the DM decide if those interactions break their game. Sneak attack was purposefully made to NOT integrate unarmed strikes. If you have a way to turn an unarmed strike into an armed strike, it may cause a problem. If you don't think it does, or you can handle it by increasing enemy difficulty, etc, then go for it.
A note on unarmed strikes(from guildsbounty and Miatog)
It is important to note that monk unarmed strikes are not necessarily nor are they always a punch. The strike can come from an elbow, knee, head, etc - which is why the Monk doesn't need a free hand to make use of their unarmed strikes.
In addition, once you add a finesse weapon to allow Sneak Attack, you are no longer making an unarmed strike. You have armed yourself with a finesse weapon.