Q: Can we get pre approved for a loan in the next 3 months?
A: So far nothing you have said indicates you would not be able to be approved.
However what is on your credit that is bringing your scores down to a 635 & 650 would need to be gone over, as that is equally as important as the credit scores themselves. Also, account disputes often need to be ended prior to having your credit checked, not always if you are applying for an FHA or VA mortgage, but they do need to end if you are planning on using Fannie Mae or Freddie Mac conforming financing.
With FHA financing you'd just need to put 3.5% down, which even on the $450k sales price is only $15,750. VA financing is 100% financing in case you or your husband are a Veteran. Conforming financing can just require at least 3% down, but it's usually recommended to put at least 5% down for better financing terms.
If you were considering a loan term longer than 15 years, then FHA & VA financing would result in the lowest interest rates since they aren't so sensitive to your credit score. Conforming financing is very sensitive to your credit score - to put it as an example, if you were getting an FHA mortgage with a 635 FICO score you could expect your interest rate to be about ~4.5% with no points (not a quote, just illustrating where rates are at with most lenders today). With Conforming financing, a 635 score, and 5% down, the rate would be approximately .25% higher plus you'd have to pay an additional 2.25% in points (that is 2.25% of your loan amount) just to get the .25% higher interest rate.
Loan term of 15-years or less (read: 15-year fixed or shorter term), then conforming interest rates are the same .25% higher than FHA & VA interest rates, but since conforming interest rates are not sensitive to the score at 15-year terms or less, there wouldn't be the 2.25% in points to get the conforming interest rate, it'd be 0 points. Since your income level is pretty high compared to the amount of mortgage you are looking to finance, a 15-year term option may be something to strongly consider.
With FHA financing you have an annual mortgage insurance amount (divided into monthly payments) of 1.1% to 1.15% (.25% to .50% on a 15-year term or less), as well as an upfront mortgage insurance amount of 1%. So the mortgage insurance can really add up over time. VA financing doesn't have any monthly mortgage insurance, but it can have a VA Funding fee of 2.15% (exempt with most service related disabilities).
Conforming financing requires private mortgage insurance (PMI) when you are financing over 80% of the home's value, however you have a few different options for mortgage insurance -
#1 the standard monthly amount that most people are familiar with (this is only guaranteed to drop off once you pay the loan balance down to 80% of the home's value when you obtained your mortgage, some lenders may allow you to get an appraisal before then to prove you have the 20% equity, but it's not required for the lenders to do)
#2 an upfront amount you pay instead of the monthly amount (this amount is usually equivalent to 2-3 years of #1, the monthly mortgage insurance, and so if you are scheduled to pay the monthly mortgage insurance for many years based upon your initial down payment and how long you anticipate to have your loan balance above 80%, this option can save you a lot on the mortgage insurance over the life of the loan)
#3 a higher interest rate where you don't have to pay either the upfront amount or the monthly amount (but that higher rate is for the life of the loan, this is usually a good option if you only plan on having the mortgage for a short period of time, 2-3 years, and you know you will be paying it off or refinancing, since you aren't paying the "higher interest rate" for very long).
Those PMI requirements currently call for having at least a 660 qualifying score (even higher if you are putting less than 10% down), meaning the lowest middle score out of all applicants on the mortgage - and so your 635 & your husbands ~650 scores would be below that threshold. Perhaps after your round of disputes you are doing it'll eliminate some of the delinquent items on credit and your score could get up there. On July 11th a new PMI program is coming out that only requires a 620 score up to 97% financing.
If you can find a home at http://www.homepath.com
(Fannie Mae's REO inventory), then with a Fannie Mae HomePath financing program you do not have to pay PMI, but the rates adjust upwards to reflect that - it's similar to option #3 above.
So as you can see, there are many options to consider, and with your credit still being worked on, what is a better option right now may not be the better option after your scores change (hopefully for the better).
If you need help, have more questions, or want more information, feel free to let me know.