Four days is a lot of time for most people to spend with their own family, much less someone else’s. Of course, most people who are in a significant relationship will be dealing with their partner’s family to some extent. These exchanges can often be fun and a great way to hear interesting stories about your current love interest.
If you and your boyfriend live in separate houses, you are definitely at an advantage in dealing with the situation, though some of the same strategies can apply even if you are living together. From your question, it sounds like he has his own house and so I will assume you don’t live together.
The key to creating a successful experience with your boyfriend’s family is to participate fully in as many of the activities as you want, keeping in mind your introverted nature and your own personal time and energy limitations. Naturally, some of these events will be much more important to your boyfriend and his family than others, so this is something to keep in mind as you think about which events you want to participate in.
Communicate with your boyfriend in advance of the visit to let him know your feelings, needs and worries. No doubt most of what you share will not come as a surprise to him, since your feelings are quite normal for this type of situation. He probably already knows that you need a balance of social time and “down time” but do gently remind him of this. Ask him which events are the most important to him and let him know you definitely want to participate in those events.
Negotiate with your partner how you might arrange to have the quiet personal time that you also need. For example, if you are spending the whole morning with the family and they are off on another afternoon adventure, maybe you can let your boyfriend know that you may decide to stay home and rejoin the family for the evening festivities. If late nights are customary in his family but not fun for you, create realistic plans about how you might politely excuse yourself and take some personal time to unwind and get to sleep at a decent hour. Ask for his support in this.
In summary, let him know how much you truly do want to get to know his family, but you don’t need to compromise all of you own needs to convince him of this. You don’t need to prove anything to him and he can probably be comfortable respecting your needs as well. Finally, don’t guilt-trip yourself about the things you don’t have energy to do; just enjoy with the activities you do with his family to the fullest and enjoy the ride! After all, it’s only four days.