It sounds like, first and foremost, you have a serious technical conferencing issue that transcends standups. I've worked in a variety of remote teams and the only time I've seen issues as bad as you are describing is when I was forced to work on 20 year old defense grade encryption technology for our 3-way team communications.
A couple thoughts:
Culture - Work at Home
When your group offers a culture of work at home, it's critical that both management and the work at home people take ownership of technical communications. The standup cannot be the place you do your technical debugging - you need some scheduled time to find a solution to conference calling that doesn't take away from team meetings and you really can't rationalize having a huge work at home offering until this is ironed out.
Sorry if that means you manager can't come in... but this is a big deal. I haven't seen teams succeed without a way to get fast verbal communication between multiple parties in a pinch. IM is great, but I've never seen it work as the only answer.
This also comes down to a commitment to purchase equipment. Most offices I've seen with a high work at home offering make the shift to providing better equipment to the end points at the cost to niceness in the office.
Conference call technology and issues
I almost wonder if you don't have a serious bandwidth issue. I don't want to get into how your phones and data services are wired, but problems on both Skype and conference calls are new to me.
I've used both very successfully including:
point to point with Skype around the world (Boston to India, California, and Canada, all using ADSL or Cable Modem at the end points, unpaid accounts) using video. And not just for conference calls, but for classes that involved a high degree of movement and a need to coordinate voice and movement across the channel. Choppy Skype suggest you have a bandwidth choke or seriously poor equipment on one or both ends.
Conference calls - it seems every office I work on uses this phone and I haven't had any problems with it. Granted, I work in a lot of big companies, so I don't know if they make any special arrangements for the conference room phone lines. The one thing I notice is that remote workers also need a good phone on their end. They may need a landline, and they need to be aware of the noise in their environment, possibly going so far as to be very active with mute/unmute.
Open plan rooms - need extra testing - different conference phones react to ambiance noise differently. You may want to make sure you buy them with a good return policy while you try them out. The noise of computers in an open plan room means that you need a phone that will muffle the white noise continuously while keeping voices clear.
This hits on another cultural aspect - work at home with standup meetings has to be treated just as seriously as stand up meetings in the office. At home workers need to plan to be in a quiet area, undistrubed, where they can focus and not have lots of noisy interruptions.
Tricks for standups across multiple spaces
I've run some non-colocated Agile teams, and I now run a standup for a not-really-Agile team where we have 2 work at home people at some points during the week. Here's my lessons learned.
Protocol needs to be clean, moderator needs to be more active - if people get long winded, cutting them off is even more important, because you can't tell if the on-the-phone people have totally glazed over or are looking intently.
Call on people - you can't tell what the "circle" is, so call on people - it wakes up the people on the phone. Also get the whole team into the habit of naming the people they want an answer from. "I'm having a problem with X, Bob, Sandy - any ideas?"
Make sure everyone, everywhere gets equal time
Get people condensed as much as possible. Just because 3 people are at home, does mean the 3 people in the office should not huddle around a phone/computer. It helps with conversational traffic flow and reduces the number of end points dialing in, which improves call clarity.
Make sure everyone shares phone ettiquitte - muting rules, ways of eliminating the "everyone speaks at once" problem, and other things - you may even end up with a team "how to conference call" set of tips.
Don't let your remote workers be 100% remote - they need to plan a time to be around the in the office folks. One thing that helps us is a "in the office day" where no one gets an ongoing waiver for not being in that day. Obviously mileage varies with the state of the team. When I had a guy on the other side of the country, he flew in once a quarter and hung out for a week or two, instead. This sounds like general policy, but it's actually crucial for standups - people need to see each other's reactions from time to time, and doing so let's them form a mental picture of the guy on the other end. This empathy is what you miss most when trying to run a standup efficiently with remote people.