Are you okay with delaying the home purchase? If so, then yes, max out the Roth accounts. There are no tax benefits "today" but those funds, including any growth, will be exempt from all future income taxes.
If you plan to use the money in the next year, I would probably stick it in a 1.0% savings account and call it a day. The 90/10 route is probably more trouble than it's worth. If this were 3-5 years away then maybe...
Yes, your account growth (if you have any) will be taxed at ordinary income levels if you cash out the betterment account before hodling it for 1 year.
Net: Max out the Roth for both you and your wife, keep the rest in an online savings account at 1.0% interest until you have enough for your downpayment.
Enjoy the househunting process!