Recipes aren't the source of problems nearly as often as often as technique. In your case, it's both. Start with losing the milk. Do some googling and synthesizing your own formula out of the mainstream recipes you find all over the web -- here, Food Network, Epicurious, and so on -- always going for the simple. It's a very good way of putting together a sort of ur-recipe out of similar formulas.
If you like, I can write one out and pass one on to you. It's something I meant to get to anyway. But, I get the feeling you don't need the whole megillah and would rather handle it without more input from me than is in this post. Either way...
Most pasta is made from flour, eggs, oil and salt -- and unless you want to get into flavoring with spinach powder, tomato powder or the like, or adding a few herbs into the dough mix. You should stick with a very abbreviated ingredient list until you're getting a texture you really like.
Use the "volcano method" to mix the ingredients and bring the dough together, as you're already doing. Knead it, as before.
Cut into pieces, if you won't be using all of it that meal. Wrap the pieces in cling wrap. Then, flatten into disc(s). Note, the discs will be better and flatter (useful when you go to roll thin) if you wrap first). Refrigerate what you're going to use, and freeze the rest. Refrigeration relaxes the glutens.
Use a pasta roller, whether mechanized or hand cranked to roll your pasta. A pin is doable, but nowhere near as good for reasons of working the dough, and uniform consistency, both. There are a number of good hand and motor driven rollers on the market. I use a hand-cranked Atlas myself -- but have to admit the Kitchen Aid pasta attachment is as good as it gets.
Depending on the width and shape desired, you may cut the pasta with the roller-cutter attachment; use a cutter (as for ravili); or in the case of wide pastas like tagliatella, use a knife. If you want pasta with a round cross section, ala spaghetti, you need to use an extruder after the knead, rather than rolling and cutting.
IMO, the lack of resting, the lack of refrigeration, rolling by pin, and the presence of milk are the sources of your dissatisfaction. Each is counterproductive, taken together -- not a recipe for success.
Good luck with this,
Ex owner/operator Predominantly French catering; ex cook at a couple of decent joints