You do not get a 1099B for that - you get 1099-R forms.

Your 403(b) rollover to a Traditional IRA would be tax free.

A distribution from that IRA will be taxable as ordinary income. If yiu are under age 59 1/2 then there will be an additional 10% penalty on the distribution.

What you did with the money is immaterial since a 2nd home is not a first-time home owner.

Enter a 1099-R here:

Federal Taxes,
Wages & Income
(I'll choose what I work on - if that screen comes up)
Retirement Plans & Social Security,
IRA, 401(k), Pension Plan Withdrawals (1099-R).

OR  Use the "Tools" menu (if online version left side) and then "Search Topics" for "1099-R" which will take you to the same place.

Be sure to choose which spouse the 1099-R is for if this is a joint tax return.
Be sure to pick the correct 1099-R type: Standard 1099-R, CSA-1099-R, CSF-1099-R, RRB-1099-R.

[NOTE: When you get to the "Your 1099-R Entries" screen where you can add another 1099-R, use "continue" to keep going as there are additional interview questions after that screen in most cases. You can always return as shown above.]

And it is not "the same withdrawal".   One 1099-R should be issued by the 403(b) plan administrator for that distribution and the other 1099-R issued by the IRA custodian for that distribution.

Would the distribution from the IRA be considered an asset I used to purchase the second home (another asset) under capital gains?  

No.  Gains and losses within a tax-deferred retirement account are not reported anywhere outside of the retirement account.