No, you are not worrying too much - we too have left Rowdy and I am a nervous wreck till we get back and see that he is OK. Sometimes it is inevitable that you have to take them with you and leave them in the hotel. Be aware though, that some hotels allow pets, but have a policy that you NOT leave them in the room alone. It sounds like this hotel does not have this policy.
It's funny, the person who mentioned getting an RV, to keep from leaving their baby in the hotel room - we have a 5th wheel and sometimes take it when we wouldn't otherwise, just for this very reason.
Good luck with the new grandbaby!!! They are so wonderful!