Struggling to come up with down payment

I hope some of you can give me good advice please.

Me, a single mom and my son in his early 20's would like to buy a home together. Currently we are renting and with interest rates so low, we can afford the monthly payments on a house but coming up with the downpayment is a big problem for us at the moment.

We are pre approved for a loan big enough that will cover the amont we need to borrow.

I still have access to a line of credit I had with my ex husband, we are on very good terms and I have been in charge of the line of credit for a long time. I can borrow about $ 7 000 from the line of credit on the short term till other monies that I can lay my hand on later comes available. The line of credit is linked to a joint chequeing account. On my monthly statements of both the chequeing account and the line of credit both my ex husbands name appears and mine.

My plan now is to borrow $ 7000 from the line of credit as part of the downpayment of this dream home we saw up for sale.

I would like to know with only 5% down can I go to my bank and draw the $ 7000 cash from the line of credit and deposit it into my son's account where it will show up as just money.

My question is : Will the mortgage lender be able to see or trace that $ 7 000 back to my line of credit? My understanding is that for a downpayment you cannot borrow from your line of credit.

I am worried that if I wait for other money I have that will be available to me in about 8 weeks, this dream home will be sold. Thats why I was thinking for the short term to borrow against my own line of credit for the downpayment.

I am asking this as recenly when we applied to be pre approved i got the shocking news that I had no credit rating ! I have been using the line of credit and a credit card I had jointly in my ex husbands name for years and have been paying it off montly on time and yet when they did a credit rating on me nothing showed up for me ! Since then I got my own credit card and are building up my own credit score.

On the credit card I was using previously on the monthly statement only my husbands name appeared yet I had a card that was joined to his.
Now I am wondering when they investigete me now to be approved for a loan will that line of credit show up that we have jointly and will a paper trial show up that shows I am using some of the line of credit as a down payment?

Thank you kindly in advance for any response.