Brands & types of heat mats differ considerably, but I've never heard of one splitting- that's unsafe & hopefully you aren't still trying to use it? It belongs in the trash, UNLESS you have your receipt & the product has any sort of guarantee??? If so, I'd return it for sure!
FYI, I've mostly used Flexwatt (controlled, of course) & mine has lasted way over 20 years. The only few that ever failed got bent during moving. (Flexwatt is very thin & easy to damage if not careful, but holds up great when you take good care of it- there are similar products on the market just like it now, under different brand names. And that's just one type of heat mat of course.)
A "cool side" with a heat lamp doesn't sound like it qualifies as a "cool side" unless your house is quite cold?

What are the temps (lowest & highest) in this tank? You can injure or kill a snake with too much (or uncontrolled) heat, not to mention it's not safe for you either- heat mats allowed to over-heat can start a fire. You truly need to get this "right" & quickly.
And
