Competitive and hitting in DD's cousins - Need Help!
I think it's very common for that age to say "I'm faster than you", "I can hop more than you", etc...It sounds like your dd is somewhat sensitive and maybe you just need to talk to her about it...also when your niece wants to be competitive, encourage them to be co-operative instead. Like if she says "I am so fast, I can outrun you from here to the tree" (a very normal thing for a kid to say at any age), you can say "Wow, both of you are so fast that I bet you can make supertime if you do relay" (and explain what relay is and see if they can beat a stopwatch TOGETHER cooperatively. I think it teaches your niece how to have fun without being best and teaches your daughter another tactic apart from getting frustrated and feeling 2nd best when someone is being competitive. As far as your nephew, if it's been a while you've seen him, perhaps he's grown out of that stage, but regardless, you can add one more tool to your arsenal, teach your dd to stand up for herself. She is older, so she may sense when this child is about to get mad and avoid it OR if he starts hitting her, she can ROAR loudly "NO, STOP". It's basic self defense...because she needs to have some idea of how to defend herself, and especially with a younger child who is probably weaker and less mature. She could also tickle him or challenge him to a race or try to distract him or even sit on him to stop him. It almost sounds like you try to fix all the interactions between your dd and her cousins, and (I'm really not attacking you, I promise) it robs your dd of a chance to learn those skills herself. She may need some ideas on what she can do (especially if she's an only) but she also needs a chance to do it.
Again, I hope you don't feel like I'm attacking you - it's frustrating to see your dd on the receiving side of negative attention, but rarely is it that it's all one way...I see that when my kids play with others, how often the parents only seem to notice when my child is poking another one with their finger (not in any way that would hurt), but don't notice when their child is trying to poke mine with a stick in his face. I just see that kids need to learn skills to deal with kids that are close to their age and that it makes them stronger rather than having their parent or other adult always step in to fix the problem.
Ok, got ya! Yeah, there's not a solution for every situation. I have some friends whose kids like to make everything into a race (even how fast you're done in the bathroom!), and it seems that is encouraged by the parents as a way of making them do things quicker. I chose not to do that with my kids, because I didn't want them to have bad feelings toward each other...as I remembered how my nephews were always set in a race against each other as far as "oh, look child A is going to eat his supper faster than you" "uh oh, B is catching up to you...better hurry". If your sister doesn't do that, then your niece may also be trying to play the oldest child card...my ds1 always likes to say he needs to have more of anything than ds2 because he's older. So maybe your niece is also trying to establish a pecking order...and maybe it would help if you would invoke her help ... as in, "You are really good at unbuckling. You are X months older than DD...maybe you can show her how you unbuckle and teach her?" I do that with my 2 boys often, as in make the older one responsible for helping the younger one...because we are one family and we are together, and we can all accomplish what we collectively want that much faster/better if we help each other, whether it's helping ds2 put shoes on or filling his sippy cup. Sounds like your nephew may just be bored out of his mind if you're driving for an hour somewhere - that's a long time for an active child to be in one spot buckled...what if when he gets antsy and starts to cause trouble, DD (if she's sitting next to him) pulls out a picture book about something he really likes and talks about the pictures? It'll give her the older sister feeling too...and may help keep your nephew focused on something apart from hitting for a little while longer. Good luck....nothing really works 100% of the time...I wish there was a magic wand I could wave when my kids are fighting with each other...but I think eventually they'll grow out of it. I still remember fighting with my brother and dh remembers fighting with his sister and how annoying that was to our parents :)
Helping your DD figure out why she is crying may also help. My DD used to cry at the drop of a hat and Deconstructing the statements that made her cry afterwards, once conflict was gone, helped her to slowly start applying that to real life. It took many conversations and time to move her away from that sensitivity though.