I am very familiar with cool season grass mix lawns, not so much with warm season grasses. I've never heard lawns having both types. One is a cool season grass (Fescue) which can go dormant in the severe heat and the other, Bermuda, is a warm season grass which goes dormant in the winter. They are such different plants with different needs different colors, different textures. I just do not see the rationale for mixing the two types for a lawn. I could easily see how a mix would cause a patchy lawn.
The worst part is Bermuda needs to be mowed short (1") and the Fescue needs to be mowed long (3" no shorter). The reason for this are the different root systems. Bermuda is shallow rooted and Fescue is deep rooted. To support the genetically dictated large and deep root system of cool season grasses, that plant has to have enough photosynthetic top growth. Thus mowing no shorter than 3". Bermuda does best with a buzz cut...3/4" to 1 1/2". How the heck do you chose which species to cater?
It seems that you aren't alone that quite a few people do this and I am having the toughest time with the logic. We also need to know the variety of your Fescue. Is it Chewings, Red, Hard or Sheep Fescue for fine Fescue...or Tall Fescue? Probably tall Fescue as it is the most heat tolerant of the Fescues. But it could be Hard Fescue as well.
I never use pre-emergent herbicide. Especially if I want my grass seed to germinate. If one had one type or the other and not both grass species I'd be able to tell you how to prevent weeds in lawns easily. One way to prevent weeds is by watering practices. By watering deeply, then allowing the lawn bed to dry out (the time to water is when the grass starts dehydrating you are able to see your footprints stay down on your lawn as the grass doesn't have enough moisture to pop back up) weeds that have germinated will be killed by too little water available as they have a shallow root system as well. Another way is by mowing 3" no shorter and that shades the soil, conserving water with lower evaporation, not allowing weed seeds to germinate at the same time that height supports the large root system. Watering deeply and infrequently TRAINS your cool season grasses to grow deeper thus becoming more drought tolerant. They are able to get at the moisture 4-6" below the surface when shallow rooted, newly rooted weeds can not and your lawn won't go dormant during high temperatures. Your Bermuda grass is shallow rooted, but dense and designed for severe heat. It is very competitive and would be best as a monocrop.
Hard Fescue plus Bermuda Problems
Ahhhhh. Finally found an article that pulls this together. This mix is great at first, Bermuda grass actually out competes and thus a patchy lawn is NORMAL. Shoot, I would get a sod cutter and get rid of all your sod and start over again. Just use Bermuda grass. How hot does it get over there in Kentucky? I've lived most of my life where the temperatures get over 100 F and 20 below in the winter and all I've ever planted were cool season grasses. I am wondering if you could go to an all-cool season grass mix for your lawn. Greener, cooler, easier to maintain...only because I am very familiar with cool season grasses which are usually a mixture of 4 or 5 species and they stay mixed as a crop. Easy to mow at 3"-4" and never have to worry about going dormant, weeds. All one needs to do is fertilize 3-4X per season, water deeply and infrequently, mow ON HIGH (now that might be tough as most mower decks do not allow this height, I have my mowers custom 'raised'), keep blades SHARP and aerate once per year. Otherwise, Bermuda grass seems to be fine as a monocrop. Same watering practices, mowing once per week minimum but at 1" height.
I hope this article helps you to make a decision, perhaps you'll figure out a better solution, or someone else on this site will know Bermuda grass better than myself...rather Bermuda Grass mixed with Fescue Lawn crop. This makes no sense whatsoever for my thinking. Bare spots are your problem as weeds are opportunists. Bare spots provide sun, soil, water...for seed germination.
And grass seed is usually ready to mow at 11 days +/-. Bag your clippings and use on your plant beds spread thinly. Growing baby grass in an established lawn is again at odds for maintenance. Watering shallowly and frequently (4 or 5 times per day) is necessary to keep those babies moist. Then you need to TRAIN them to get their large root systems before watering as you would for a mature and trained lawn. Seriously, the lawn is a beast that needs a trainer and correct feeding (don't use fast release fertilizer)...I am not a granola type, chemicals are chemicals but in this case, those organic, extended release, bit more expensive lawn fertilizers are worth every cent! They come with thatch eating bacteria, mycorrhizae critical for symbiotic root support on all plants, slow release to eliminate the stress of a high nitrogen HIT, slower top growth after fertilizing and I've gotten by just fine on 2 applications instead of 4! The only brand I am familiar with is Dr. Earth's Lawn Fertilizer. There are more brands very similar, just shop ingredients and price.
I had to learn how to care for this BEAST and this question was a stumper for me.