So here's what I'd do if you want to stick to a Hyatt Hotel:
1) See if there's a Prive rate, which you need to book through a travel agent - there are several on FT who you can reach out to, but I use bcosinteno who is great.
2) If the Prive rate is less expensive than the publicly available Member Rate or whatever other rate you would use, then book Prive for both rooms. If Prive is more expensive than whatever other rate you would normally use, then just book it for the 2nd room (as long as it's not significantly more expensive)
3) Call/Twitter/Email Hyatt Concierge to apply club access award to the 2nd room. You won't need one applied to your room due to your Globalist status. You can also apply TSUs if you like.

The only way to 100% ensure your parents benefit from your status is to book Guest of Honor. However, since you want to pay cash, that's not an option. The next best thing is to book them a Prive rate, which gives them basically all the same benefits as Globalist.
Keep in mind that Prive benefits also stack on top of your Globalist status for you. Thus, you'll get everything you're supposed to as Globalist, plus the ancillary credit and welcome amenity. The final option is to see if there are reports on FT of hotels providing Globalist benefits to multiple rooms, which happens sometimes, but I wouldn't 100% bank on it.

As for your question on base points for lifetime status... yes, you will earn the base points (and bonus points) on the 2nd room. You won't get any extra elite night credit for the second room.