70 amp service from 200 amp main
TLDR: 1/0 aluminum with #6 copper ground wire.  And yes, you can run straight through with either cable or wires-in-conduit, however, if you splice, you need a really big box. 



Hold on. I'm a little unclear on your power requirements. 

Provisioning


It seems like you're kind of armwaving the hot tub, but most hot tubs seem to take a 50A or 60A service, so let's be hopeful and call it 50A (provisioned). 
The sauna with 8000W heater needs to be derated 125% to 10,000 watts, so we must provision 41.6 amps. 
The 1000W wall heater also needs a 125% derate, so 1250 watts or 10.4 amps.  
The tandem 20A breaker, you didn't say that that's for and I'm not sure a tandem is a sensible choice since it puts both 20A circuits on the same pole, requiring us to provision as much as 40A for them.


If you wanted to tandem the 20s to squeeze in to 8 breaker spaces, that's the road to perdition. Breaker spaces are cheap, replacing your panel because you cheaped out on breaker spaces is ex-pen-sive.  For a few latte's you can kick up to a 16-space or 20-space (not circuit) panel and never have to worry about spaces.  The extra room allows us to put those two 20A circuits on opposite poles.  They sit 20A side by side instead of stacking, so we only need to provision 20A for them. 

The 15A circuit I assume is for lighting, and in the LED age that'll be negligible, so I'll provision 0A for that.  (by the way, if you don't want to have to buy two sizes of wire, you are totally allowed to do lighting in #12 / 20A). 

Siemens makes a $30 generator interlock for that panel I linked. It ties two common 2-pole breakers so they can't be on at the same time.  If those breakers are for your hot tub and sauna, that means you only have to provision power for one of them :)

So, provisioningwise, with the two 20A circuits on opposite poles (not stacking) I see 50+41.6+10.4+20= 122 amps. Whoa.

Now if we interlock the hot tub+sauna, then 50+10.4+20 = 80.4A, call it 80A.   

Wire sizing - distance and metal

Upsizing wires is appropriate for long distances, but that's not a suicide pact.   It pays to spend some time with a voltage drop calculator and figure out what happens to voltage drop when you use various size wires.  The "rule of thumb" says 3% is an ideal, but Code is more concerned with 8% overall. So let it slip past 3% a good distance if not doing so will waste money. 

Speaking of wasting money, at #6 or larger it starts to become time to look at aluminum wire. My answer here really drives that home (they have a 260' run @ 100A, but hold that thought). 

If this were a short distance and your load were really 70A, you could use #4 copper or #2 aluminum ($486 or $210). We are using Table 310.15b16, and we're required to work out of the 60C column because we are less than 100A.

But this won't do, for two reasons. First your load is really 80A+++. And second you need to make a wire-size bump because of the distance.   So we look at the very next size up, #3Cu or #1Al ($594 or $312), good for 80A @ 60C.  But a funny thing happens here.  At 100A, we're able to use the 75C column. And these same 3Cu/1Al wires are good for 100A @ 75C.   So we get a free bump to 100A. 

Mind you, the "free bump" doesn't have any effect on our voltage drop.  The voltage drop is still a big deal.  So what if we make one more bump, and what does that do to price? So we bump to 1/0Al ($354). (copper is over the moon at this point). 

1/0Al is good for 120A @ 75C.  They don't make 120A breakers, so we round up to 125A.  So we can actually breaker this thing for 125A and power everything, no interlock needed.  How bad would voltage drop be at that point?  My calc says 3.10% voltage drop, red alert, it's over 3.00% - lol just kidding, 3.1% will be peachy.  We can power everything.  

But wait. Aren't we paying extra to power everything?  Yeah, our previous option was the #1 aluminum for $312.  $354 - $312 = $48.  We're spending 48 extra dollars to fully provision all the power we'll need. Sounds like a good investment to me! 

So you're going to spend about 70 extra bucks listening to me... buying much larger panel and wire.  What's this whole project, about $10,000?  Don't worry about $70.  Besides, if I steered you away from copper, I just saved  you about $300.  

Routing

Can it be run in one continuous shot?  Absolutely.  If you want to splice it at the transition, that's allowed, but it needs to be inside a junction box and the junction box needs to be fairly large, practically gutter sized - ask a separate question about that. 

In either segment, you can use either cable, or conduit.  With conduit you can use either cable or individual wires. Individual wires (THWN-2 or XHHW-2 or USE-2/RHH/RHW-2) must be inside conduit. For practical DIYing, use 1-1/2" conduit.  Cable is very stiff, so it requires a bigger 2" conduit to be DIY friendly.

Underground, direct burial cable needs 24" of cover over top of wires. Conduit requires only 18" cover, or merely 6" cover for expensive Rigid and IMC conduit (12" under driveways). 

My own preference is conduit the whole way, however theft is a consideration: a lot harder to steal direct burial wire. 

Grounding

With two services in such close proximity, you really need to make sure your grounding is absolutely tip-top.  There is a genuine likeihood of the ground potentials being quite different between the two services.  This is no place to be playing "cheapie" games like forgetting the ground wires in each feeder and thinking the ground rod will suffice. 

Imagine there is 120V ground potential difference between the service that supplies the hot tub and the service that supplies the building... they are different transformers, surely.  That means between the local ground rod at the hot tub, and the local ground rod at the building, there could be 120V of ground differential 10' apart from each other.  That will create a ramped voltage on the ground, meaning different voltage under each foot!  Now if that was a product of transformer leakage, the voltage difference could be 2400V, and that will kill you.  

This is nothing to toy with, especially around water. 

So I would link those two ground rods with a buried copper ground wire. Or simply both tap the same rods.