Blend with specified distance is not acurrate

Piter,

I believe that this whole thread has been driven by the woolliness of the concept of distance, which have made us all give to the right answer to the wrong question:

More specifically, it is like the question: how far is it from here to there?

In our trying to suggest solutions we have all worked on the understanding that you are measuring distance along the path, which is the requirement in (almost) all other cases, whereas you are measuring distance across the Artboard/Workspace, thus corresponding to the equally significant difference between distance along the road(s) and as the crow flies.

As I (mis)understand it now, the solution is of a completely different kind.

Smart Guides being your friends saying when you are within snapping distance, one way is to:

1) Create your dot circle as desired, then create a nostroke/nofill circle with a W = H = twice the desired centre to centre distance exactly on top of the dot circle, then Ctrl/Cmd+G to Group them (you can keep the original somewhere convenient for further use and work with a copy, or just grab the set for the next path);

With this, any spot on the nostroke/nofill circle is exactly the desired distance from the centre of the dot, and therefore it acts like one ruler working in every direction at once;

2) ClickDrag the set by the common centre where Smart Guides say centre, first to the start of the path (Smart Guides saying anchor), then for each following dot Alt/OptionClickDrag (thereby moving a copy) to the next spot where the current circle crosses the path; where Smart Guides say intersect; you can get hone in by watching the nostroke/nofill circle getting close to the centre of the former dot, and you can use the Bounding Box of the former dot as a guide on vertical/horizontal parts, but overall it is easy to get close enough be eye and then move about till Smart Guides can help.

Edit: You can see the difference clearly here, and also insert other places of your own choice:

https://www.freemaptools.com/how-far-is-it-between-london_-uk-and-glasgow_-scotland.htm

Edit edit: If you (still) wish to have a learger dot circle at the start and end, you may start with the following:

0) Create your larger start/end dot circle as desired, then create a nostroke/nofill circle with a W = H = twice the desired distance to the first normal dot circle (or with a W = H that gives you the desired spacing bewteen the (outer bounds of the) dot circles) exactly on top of the larger dot circle, then Ctrl/Cmd+G to Group them (you can keep the original somewhere convenient for further use and work with a copy, or just grab the set for the next path), and then ClickDrag it by the centre to snap to the start Anchor point;

Then go on with the normal circle set as in 1) and 2), and then:

4) Alt/OptionClickDragging the large circle set by the centre to snap to the end Anchor point.

Well, I've tried the main ways to achieve the shown result (main stroke 4,3 px, white dots 2,3 px, gray around 4,3 px, distance between white dots 30 px). So they are:

1. Dashed strokes

2. Blend with specified distance

3. Pattern brush

But anyway you will need to add the bigger internal points for main stations.

Can you please make a list of what you need this to do?

1. Horizontal and vertical lines

2. 45° lines

3. Curved lines?

4. Dots need to be exactly on corners - when the line makes a turn?

5. Lines with dots need to be editable - so you can move them?

6. Dot distance needs to be adjustable in case you need it?

7. Dots always look the same - or are there different sizes?

8. When map is done, you want to expand it and put text next to the dots

9. Distance of 50 pt between the dots

... anything else?

What I don't get is your complain about the alignment of dashes on corners. Since your lines need to have a specific length (mutliple of 50 + dot), this should always work as long as you draw a perfect path.

so, you need some independent circles placing horizontally, vertically and in 45° and the line under them?
If yes, you don't need to build such complex constructions.

1. Draw the 15px circle

2. Double-clicking on Move tool in Tools panel activate the Move dialogue. Set horizontal distance as 65px (15px diameter and 50 px distance), click Copy.

4. Using Ctrl/Cmd+D, create the needed amount of circles.

5. Repeat the Move dialogue step using Polar coordinates (45° angle and 65px distance)

6. Repeat Ctrl/Cmd+D.

7. Do the same way for any other angle.

8. Draw the line between circles centers, set its width/color and put it under them.

With Pattern Brushes and various multiple Stroke options, I think you have some excellent solutions to your spacing problem. But I'd like to get back to the question as to why Align Spacing is so drastically different than Blend Spacing.

I believe the Blends are measuring the distance between the centers of the circles, while the Align to Key Object with Distribute Spacing is adding the space between the objects (the gap).

Oops, sorry, the screen grabber did not take panels. So, here are the needed screenshots.

Some moments:

1. Add the invisible rectangle under the gray BG to unify all the items heights.

2. When create the brush, select Add Space to Fit option to keep the path items length as 20 px. After drawing the line you will need to correct it a bit (slightly move the Start/End points) to close the gaps.

3. All sizes will be kept accurately if your line have a standard width 1 pt.

Piter,

What happens if you select the path and then click the icon right above the 3rd Dash (Preserved exact dash and gap lengths) instead of the currently clicked icon right above the 3rd Gap (Align Dashes to Corners and Path Ends, Adjusting Length to Fit), see the following link for explanation)?

https://helpx.adobe.com/illustrator/using/stroke-object.html#create_dotted_or_dashed_lines

The latter currently clicked option corresponds closely to using a Blend, in this case trying to be too helpful, regulating what you need unregulated, thereby undoing your trying to get away from the overly adapted dashing.

In any case, Anna suggests a good way.

in addition to Jacob's answer: 
Lines with such hard turns are njt very good as the uniform-stepped blends, the distance more or less depends on curvqture/

So, you can use 2 ways.

1. By Appearance panel, the way described by Jacob

2. Create a pattern with a dash and a dot on a gray bg, something like this:

and a point for starting/ending:

Add them to Swatches and create a Pattern brush by Brushes panel:

make sure your details are consistent by their sizes.

Piter,

It is difficult to see how you get such a great difference in your first screenshot, but based on the second (needed) appearance, you may use another approach, namely multiple strokes, more or less as folloews:

1) Create the path with a black Stroke and a Stroke Weight corresponding to the outer bounds;

2) In the Appearance palette flyout Add New Stroke and set the Stroke Weight to the width of the round white dots and set Round Cap, then apply Dashed Line with 1st Dash = 0 and 1st Gap = the desired distance (20 px); this ought to give you the white dots correctly;

3) In the Appearance palette flyout Add New Stroke and set the Stroke Weight to the width of the white lines and set Butt Cap, then apply Dashed Line with 1st Dash = 0 and 1st Gap = the distance between the dot centre and the line start/end and 2nd Dash = the length of the visible line and 2nd Gap = 1st Gap; 1st Gap + 2nd Dash + 2nd Gap = the desired distance (20 px); you can adjust to best fit, remember to keep 2nd Gap = 1st Gap.

With this you ought to get the desired appearance regardless of the length of the path, the error occurring at the end.

If you need a larger starting end as shown in the line.png, you can simply add a white dot on top of a black dot centred on the first dot/start of path.