If your midwife can do all the basic neonatal that you want (any tests, etc.) and follow up with such things as newborn jaundice and so on, I wouldn't go in very soon at all. My midwife was great, and we got checkups up to one month. We went to the peds at six weeks for vaccinations (yes, we vax, not saying you have to/should, that was our decision for a number of reasons) and overall check-up for before leaving the country. We never got the hearing test, though it was recommended.
A few recommendations:
1) Meet the ped before you need to bring the baby in. Talk about everything. Make sure you see eye to eye on the important things, the main principles. IF YOU DON'T GET ANOTHER PEDIATRICIAN. You do NOT need a pediatrician that has a totally different worldview. Do the pre-interview! That way, you will not get grief for anything. Any pediatrician who is going to give you grief should be crossed off the list. Be willing to drive far. You're going to have to wait forever in the waiting room anyway. It's worth the drive.
2) Talk to your midwife about all the neonatal care she is licensed and qualified to give, what is available, what is standard, and what she recommends for you. Look at how much of what is recommended compared to what she can provide. The recommended, not provided stuff is what you need to see a pediatrician for (if you take the recommendation). Then look at when it needs to be done. Hearing tests, for example, can usually wait, and all vaccines can wait.
3) If the ped cannot come to your house, and you can't find one who will, you could also see if there is another midwife who can provide neonatal care at your home, as an assisting midwife under the contract you have with your existing midwife. A home visit would be ideal!