It sounds as though you have Dr. Huey root stock instead of Queen Elizabeth or Mr. Lincoln. Look at the link below to see if that is your rose. You'll need to follow all that crazy growth down to where it begins to make sure it all comes from below the bud union, where the named roses you bought were budded on to the root stock to produce the plants. Once Huey starts, he's VERY difficult to get rid of. It might be easier for you to kill him off by carefully painting on a weed killer, being careful not to get any on your Iceberg. Once he's dead, you can dig out all the remaining plant parts and replace your two bushes with new ones, hopefully, without any root stock suckers. Kim

Here is a link that might be useful: Dr, Huey

If the 2 roses (Queen Elizabeth and Mister Lincoln) are now producing red roses that look identical, then you have probably lost both varieties and are now seeing growth from the rootstock -- and that rootstock is probably Dr. Huey. I'm linking to a photo of Dr. Huey. Check to see if the roses you're now seeing look similar . . .

Here is a link that might be useful: Dr Huey @ HMF

Oh man! I think the Dr. Huey is it. That is a bummer. So I should just dig them out and look for new rose bushes to plant there? I don't want that to happen again! Rookie mistake? or does that just happen? I've been feeling something was wrong with both of those plants for a few years...last year was a sign, but I waited to see how they bloomed. I really like the way the iceberg does. The stems are more gentle. Can I plant something similar to that instead?

They probably were not planted deep enough. In zone 5 the bud union should be planted several inches below ground level.
Olga

Yes, if you see only Huey blooms, Abe and QE are goners, and you should dig out Huey, which is not a very good garden rose (blooms only once and gets diseases).

The swelling where the canes diverge is the place where the scion (Abe or QE) is physically attached to the rootstock (Dr. Huey). There is no blending of varieties.

If a rose is not fully cane-hardy in your climate, you have to protect the graft (aka bud union) from winter kill, or else only the hardy rootstock part survives. Plant your grafted roses so the top of the graft is a couple inches below grade. If there is no snow cover, push some extra mulch over the crown for the deepest part of winter only.

What you like about Iceberg is its leafy, relaxed, shrubby quality compared to the sparse upright growth of hybrid teas and similar modern roses. There are lots of roses of that sort, though garden centers stock mostly hybrid teas. Many shrub roses are hardier than Mr. Lincoln, too. One of my favorites is 'Earth Song', a great bloomer and zone 5 hardy. Click "photos" tab at the link.

Here is a link that might be useful: http://www.helpmefind.com/rose/pl.php?n=1695

Thank you all for helping me figure that out. I never would have known that is what happened. I really just want to dig out and plant other shub roses. How long after I dig those out do I wait to plant something new?

Reading through other posts, it sounds like people are also using a Round up to kill any leftover roots. So dig it out, get out all roots I can, Pour some Round up or Shrub killer on the ground there? Or do I really need to do that?

Can't find Earth Song on some of the local nursery websites. Any from this that you recommend?

Here is a link that might be useful: Phelan Gardens Shrub Roses

If Iceberg is doing well for you and you like it, there are also Brilliant Pink Iceberg and Burgundy Iceberg, both color mutations of the original white and both should be as easy to find most places as the white. Kim

Here is a link that might be useful: The Three Bergs

NO! Do NOT use RoundUp.
The Roundup will do far more harm than a few leftover root fragments could ever do!

Just dig the plants up, and remove all of the root material you see. Any small, remaining feeder roots will die.

Dig a NICE BIG HOLE. If you dig a big enough hole, the old roots will be gone.

Take your suggestions on what to plant from people living in your zone (or colder).

Jeri in SoCal

Kristie, from Phelan's, go with either the Easy Elegance, Knock Out or Morden series of roses. They are all under the "shrub" category and the series names are listed at the bottom of each rose page. Those are the ones most likely to endure your climate from that group. Easy Elegance were specifically bred for your type of climate and disease pressures by folks in Minnesota. The Mordens are Canadian and Knock Outs are the only ones engineered to endure all the various black spot strains in the country. If there are people you trust in your area to suggest specific ones, ask them, but based upon reports and knowledge of what the breeding and selecting goals were that went into these roses' creation, those are the ones I would suggest you look at first. Your conditions are significantly harsher than what the Austin roses were bred and selected in. I have no idea how they would hold up for you. Kim

I went through this as well. I have a hot side to my rose garden..my oranges, yellows..apricots..and this spring there was a deep reddish-purple rose..uhhhhh I knew it was Dr Huey...there was no reds planted there!