Uh...not so fast thar, pard. Those SS braids are over a rubber hose. Rubber wears out, over time (Even NASA figgered that one out, after Challanger). Lots of rental property over 25 years tell me hard copper lines are always more trustworthy than rubbers, even with SS braid.
I'd take the time to put in stop valves while you've got the water off, and use a copper sink supply line. I've never had one come loose, so I can't figgure why yours did. If you go with the flex lines, I'd replace 'em eveery 5 years, and turn the water off if Mom's gonna be away for more then 24 hours. (The voice of a formerly flooded floor.)