Thanks for the additional information. It is helpful.
No matter how well behaved your dog is, he needs to be obedience trained. Not only will he then know what you expect of him when you give him commands but you can control him in situations where he is uncomfortable. Obedience training does teach commands but it also teaches a dog that you are the boss and leader and as the boss, it is your job to protect him from things such as the grill and smoke. Of course, you then have to take that kind of thing into consideration and watch for smoke that gets in his face.
So work on obedience training with him. The following site is helpful in helping owners train their dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
Once he knows sit and down and a release command, you should be able to control him a little better. Don't forget a release command. Often people teach sit and down but never a release command. When a dog doesn't have a release command they end up making the decision on when they no longer have to obey which you do not want.
You have to get him used to the crate as well. The easiest way is to start putting his food in the crate and leave the door open. He'll have to go into the crate to be fed. After a week or so, he should not mind the crate so much and eagerly enter for his food. If you give him a treat, toss it into the crate as well. We want him to start associating the crate with good things. Once that happens, you can start shutting the door behind him while he eats but be sure to open it as soon as he is finished eating so he doesn't associate it with being locked in. After a few weeks he should be fine with going in his crate.
I think you should also get a nice kong toy with treat compartment and fill it with yogurt or peanut butter without xylitol then freeze it. You can use this and the crate to help him overcome his anxiety around grills. It won't be a quick easy fix but should be effective. You will have the crate a normal distance from a grill. Put your dog in the crate and give the kong treat. When he is occupied, like the grill but be prepared to put it out after only a minute or two. You are trying to keep him calm during the initial lighting of the grill. If he is calm, give him an even better threat then the kong such as a piece of raw liver or stinky hot dog piece. You will do this at least a few times each training session. Once he is ignoring the initial lighting and putting out of the grill, you can lengthen the time he needs to calm but don't move too fast. You have to only increase it by a minute or so each step. Once he is more used to the grill smoking, you can increase it by larger amounts of time. Moving too fast though can put you back a week or more.
This is an effective way to lessen his anxiety, just be sure the smoke can not be trapped in his crate if it is a closed in type. You should also invest in a dap collar for him. It helps with anxieties and uses a pheromone much like the one a nursing mom produces to calm her pups. It is very effective at calming a dog who is anxious.
Hopefully he will become adjusted to the smoke. If he can not adjust, you will need to do what is best for him and leave him at home for a period of time. Dogs are often left at home and some for as long as 8 hours at a time. Even older children are left home alone, so your dog can definitely be away from you for a few hours at a time. The crate will provide him with a place he feels safe in once he is used to it. You can leave his special kong toy in it when you leave him so he is occupied the whole time you are gone.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.