Oh, I edited my post while you were posting. So, it is a 24 hour place. Excellent! I assume your trip is quite soon?
Ketones are pretty serious: take a look at this please:
http://www.felinediabetes.com/ketones.htm
No, I would not have only one shot per day with Lantus because it is not designed to work that way. Someone else might tell you that would be okay for the short term, but I don't know enough about what that would do to ever tell someone "that's better than nothing." It's probably not, but maybe someone else here would chime in?
If she won't let anyone touch her, yes, the boarding facility is your best option.
If you could use a sitter:
You could move your shot time. There is a procedure for doing that if you feel uncomfortable with trusting someone to come to your house at that hour. Then you would have to move it back when you return. Trusting someone to take care of a diabetic cat is not easy, in general, I know. What if they say they will and don't. If your sitter is licensed and bonded that might make it more likely you can trust them.
You could also post asking for a recommendation for a sitter in your area who can be trusted with a diabetic cat.
Otherwise, I'd stick with the 24 hour facility unless it's impossible for you, but I would also sit down with someone who manages that facility, and ask these questions:
1. Will you test before every shot?
2. Will you test at least once a day at 6 hours (or 4 or 5) after the shot so that if the amount of insulin needed is different than what you have been giving, someone will notice and the vet will intervene to make it right?
3. Will you test the urine for ketones as often as possible?
4. What are you going to charge me for these services? Are they extra?
Make it seem very clear that you know about ketoacidosis and hypoglycemia, and you know how Lantus should be used. This may cause the manager, who is probably a vet, to be willing to work something out with you -- a flat fee/a package deal. Make him see that you will be boarding this cat with his facility over and over if you can get the treatment and services you need for your little girl.