Hi M.-
My daughter is also 2 so I can offer some insight...
1. Eating dinner together - This was a battle for us too. A few things I have noted is that my daughter is worst when she can't reach the table. Try a booster seat sans the straps. My daughter does not like being restrained/tied down. However, she does like the high chair which she uses at my mother's. I think it is the consistency - that is her special chair when she eats there. Make sure she has a designated place at the table and insist she eat with you. We have started to implement a 30 minute rule in which she has to eat in 30 minutes and then the food is removed. We are trying to teach her to focus when she eats.
2. Time Outs - This can be a very effective tool. We purchased a "special" time out chair. We needed 2 - one for upstairs and one downstairs. We keep it in the closet so it it not used as a play thing or toy. She gets a three chance count down - "1" Mamma asked you to sit at the table and to eat dinner, "2" Sit and Eat, "3" Time out. We use the one minute plus their age rule so she gets 3 minutes right now. If she leaves the chair, just put her back. Do not speak to the child until the TO is finished. The clock restarts each time they get up. When it is finished, we ask for an apology. Initially, we started by asking her to say "Sorry" and she would usually repeat that. Now we ask her her "sorry for what?" and she will usually say "tantraum". We will elaborate on what part of the tantraum was the problem so not listening, kicking", not sitting, whatever. Then we tell her we love her and kiss and hug her. After that we let it go unless there is a repeat performance. We try to apply TO to critical battles. I think sitting and eating with the family at the table could be one of the ones that warrant a TO. The key is consistency on a topic. So if you both agree that is an important issue in your family use it there. If it happens in a resturant or another location (like Grandma's), pick an appropriate location to implement the same steps. I have used the last step of a staircase or a footrest.
3. Brushing Teeth - This is something we started very young when she started getting teeth. We would brush them for her in our bathroom with us while we did ours. Then we got her to hold the brush and we told her mommy and daddy needed to finish. She would typically just suck toothpaste so we would use a non-floride paste. We still tell her we need to check them. We make her open wide and say "ahh" for the molars, smile and say "eeee" for the front teeth and ask her to stick out her tongue. We make any funny noise that makes her giggle for the tongue. She then takes a few sips of water.
4. Dry Spots - No experience here. Sorry. But for rinsing the water from her hair, we make her stand in the shower and hold the railing on the wall as we tell her "Chin Up" and make her tilt her head back. It works most nights. Otherwise we just deal with the tears.
Lots of luck on all these issues.
~C.