Removing concrete lip at garage
I would challenge not being able to bond a portion of a new pad to old concrete.  I have used latex based bonding liquid to skimcoat to old concrete.  If the floor has been sealed or painted, such that it won't absorb water, might require a surface grinding.

As fully supported pad over a pad, no bonding is even necessary. 

Its not clear from your information WHY a interface/overlap area is necessary (presumably IN the garage).

If removing the 'lip' is the easier option, that should be alright, unless some rebar or reinforcing lath is embedded in the lip.