My little guy gets a bottle as the last thing before we put him to bed, it greatly helps him to wind down and relax for sleep. As the teeth start coming, we realize it's important to brush his teeth, but this wakes him up and makes it difficult to put him to bed afterward.
It would probably be easier to brush his teeth before giving him the milk, but I know we'd be trading dental hygiene for a bit of convenience for the parents.
How do we handle this dilemma?
This might make your life simpler (or possibly more worrying, considering how long you may have been doing this wrong): You're supposed to brush before meals. It's technically harmful to brush immediately after, as it removes acid softened enamel.
Brushing removes plaque, not food, so you actually want to brush the plaque off before eating, as it immediately produces acid when the food hits it, so most of the damage is done to your teeth well before you brush... the softened enamel of your teeth away, increasing the damage.
So, there you go, you simply get him to brush at the start of his bedtime routine, then story, then bottle, then sleep.
Sources: The Dental Hygenist magazine and the NHS guidance on teeth cleaning.
With the baby teeth, we did morning and evening brushing, whenever we could. If they had a bottle later on at night (eg 2am) we wouldn't try and wake them to brush.
Once they would sleep for a good portion of the night we would play a game at bedtime that included brushing after their night time bottle.
Disclaimer: I'm not a parent, so this is not based on experience.
Since deworde already answered the question about when to brush teeth, I want to add a possible solution to your other question:
How do we handle this dilemma?
Dental hygiene is important to you, but you are reluctant to wake your infant up after the nighttime bottle. And after drinking milk and without brushing teeth, there will be food left in the infant's mouth during the night.
Then, what about an alternative to brushing, that removes the food? It's safer than no brushing at all, without having the downsides of brushing right after eating or waking them later at night.
Water, however, cleans your mouth with every sip. It washes away leftover food and residue that cavity-causing bacteria are looking for. It also dilutes the acids produced by the bacteria in your mouth. You’ll still need to brush twice a day for two minutes and clean between your teeth, but drinking water through the day will go a long way toward keeping your smile cavity-free.
Source: 4 Reasons Water Is the Best Beverage for Your Teeth, ADA (American Dental Association)
So after the nighttime bottle, you could try to make the infant sip a bit of plain water to remove most of the milk (and sugar etc.) from the teeth. Try to find a good amount of it, so that it's not too much (maybe a mouthful).
