Welcome to the forum.
This is just my "first impression" and may not be the best way to proceed, but here goes.
I would leave the current pond pretty much as is with minor maintenence done to the dam and spillway as needed. Leave the biggest trees for shade and remove the rest.
Then I would take all the money you intended on spending to renovate this pond and use it to build a new pond directly above this one in the watershed. If this pond gets too much runoff you could even design the new pond to accomodate what watershed is recomended for your annual rainfall. The NRCS should be able to help with this.
You will spend about the same or even less building a new pond as you will cleaning out the old. It looks like you have plenty of land and watershed to work with. A new pond has a lot of advantages over trying to rework an old one. And an old second pond works wonderful as a "trash fish" pond. The place where you can put excess fish from your main pond for a pond that is easy for kids to catch a fish almost every cast.
You could build your house pad at the same time you are excavating the new pond so the site will be settled and ready to build when you are. A new pond you have complete control over features, construction technique, and you will know the integrity of the dam. While the new pond is coming up to speed with stocking, you will have the old pond to fish. If the old pond dam some day fails because of the trees, by then your new pond will be up to speed and you can determine then to refurbish it with a cleanout and new dam or just fill it in.
That is the way I would approach it if it were my property. I've built 4 and rebuilt one pond on my home property. You can't have too many ponds. Two is better than one. I have also cleaned out two old ponds for my kids, and I'll tell you, building new is a whole lot less work and mess.
Links to my pond building experiences.
A pond dedicated to RES Building a mini forage pond Building a sediment pond Reclaiming a 50 year old pond My main pond I don't have many build pictures of my main pond because did not find PBF till the pond mainly was finished.
