will returning to a normal life help speed my recovery?
It often helps - I don't know that it makes it go faster, necessarily, but allowing yourself to start taking on tasks will create an additional layer of challenges that you can then solve - it's in how we manage stress that we move forward, and you can't increase your capacity to manage it unless you increase the stress.
In less words: using and putting strain on an injured body part is the second half of recovering full use of it. I do believe there's a lot about the brain that works the same way.
Can I set boundaries so that I can return on a limited basis and still build balance in my life?
Absolutely - and that is going to be important. Only you can know when too much is just too much - so you will need to be able to respond to overload in a way that supports your long term goals.
I think a common mistake is to go all-or-nothing with it, to think you're either on a break or you're full strength. The fact is, even the most mentally healthy and competent person is not running at 100% capacity sunup to sundown. Everyone needs to structure breaks, diversions, rest - self-care.
Write out a plan for the day. Make it achievable. And stick to it. Aim a little low, in terms of what you believe you can accomplish - you can learn where you can add more to your plate by doing that. Always have a little list of short optional things that you can do if you are feeling up to them - but you aren't planning to do them, they will be extras for times you feel good.
How do I convince my family that this is what I need to do when everyone is looking at me like it's a big mistake.
First of all, don't mind-read. You say people are looking at you like you're making a mistake. Is that what they really think? Have they said it? If not, then the truth is, you don't know what they think. You may not need to convince them of anything. It might just be about sharing your plan.
It will be worth it for your loved ones to be in the loop about how you are addressing your own re-integration into 'normal' life/routines. Not so they can help, necessarily - but more so that you can know you aren't trying to hide something or be more OK than you are.