diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 2c77b87f8efb6..2dec3b6bdebc7 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -609,6 +609,7 @@ Other Deprecations
 - Deprecated :meth:`Categorical.replace`, use :meth:`Series.replace` instead (:issue:`44929`)
 - Deprecated :meth:`Index.__getitem__` with a bool key; use ``index.values[key]`` to get the old behavior (:issue:`44051`)
 - Deprecated downcasting column-by-column in :meth:`DataFrame.where` with integer-dtypes (:issue:`44597`)
+- Deprecated :meth:`DatetimeIndex.union_many`, use :meth:`DatetimeIndex.union` instead (:issue:`44091`)
 - Deprecated :meth:`.Groupby.pad` in favor of :meth:`.Groupby.ffill` (:issue:`33396`)
 - Deprecated :meth:`.Groupby.backfill` in favor of :meth:`.Groupby.bfill` (:issue:`33396`)
 - Deprecated :meth:`.Resample.pad` in favor of :meth:`.Resample.ffill` (:issue:`33396`)
@@ -708,6 +709,7 @@ Datetimelike
 - Bug in :meth:`Series.mode` with ``DatetimeTZDtype`` incorrectly returning timezone-naive and ``PeriodDtype`` incorrectly raising (:issue:`41927`)
 - Bug in :class:`DateOffset`` addition with :class:`Timestamp` where ``offset.nanoseconds`` would not be included in the result (:issue:`43968`, :issue:`36589`)
 - Bug in :meth:`Timestamp.fromtimestamp` not supporting the ``tz`` argument (:issue:`45083`)
+- Bug in :class:`DataFrame` construction from dict of :class:`Series` with mismatched index dtypes sometimes raising depending on the ordering of the passed dict (:issue:`44091`)
 -
 
 Timedelta
diff --git a/pandas/core/indexes/api.py b/pandas/core/indexes/api.py
index e497012f23b68..922c344510375 100644
--- a/pandas/core/indexes/api.py
+++ b/pandas/core/indexes/api.py
@@ -8,6 +8,8 @@
 )
 from pandas.errors import InvalidIndexError
 
+from pandas.core.dtypes.common import is_dtype_equal
+
 from pandas.core.indexes.base import (
     Index,
     _new_Index,
@@ -213,14 +215,41 @@ def conv(i):
 
     if kind == "special":
         result = indexes[0]
+        first = result
+
+        dtis = [x for x in indexes if isinstance(x, DatetimeIndex)]
+        dti_tzs = [x for x in dtis if x.tz is not None]
+        if len(dti_tzs) not in [0, len(dtis)]:
+            # TODO: this behavior is not tested (so may not be desired),
+            #  but is kept in order to keep behavior the same when
+            #  deprecating union_many
+            # test_frame_from_dict_with_mixed_indexes
+            raise TypeError("Cannot join tz-naive with tz-aware DatetimeIndex")
+
+        if len(dtis) == len(indexes):
+            sort = True
+            if not all(is_dtype_equal(x.dtype, first.dtype) for x in indexes):
+                # i.e. timezones mismatch
+                # TODO(2.0): once deprecation is enforced, this union will
+                #  cast to UTC automatically.
+                indexes = [x.tz_convert("UTC") for x in indexes]
+
+            result = indexes[0]
+
+        elif len(dtis) > 1:
+            # If we have mixed timezones, our casting behavior may depend on
+            #  the order of indexes, which we don't want.
+            sort = False
+
+            # TODO: what about Categorical[dt64]?
+            # test_frame_from_dict_with_mixed_indexes
+            indexes = [x.astype(object, copy=False) for x in indexes]
+            result = indexes[0]
+
+        for other in indexes[1:]:
+            result = result.union(other, sort=None if sort else False)
+        return result
 
-        if hasattr(result, "union_many"):
-            # DatetimeIndex
-            return result.union_many(indexes[1:])
-        else:
-            for other in indexes[1:]:
-                result = result.union(other, sort=None if sort else False)
-            return result
     elif kind == "array":
         index = indexes[0]
         if not all(index.equals(other) for other in indexes[1:]):
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 187fa2f3aa1aa..5a3da9b65d03b 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -387,6 +387,13 @@ def union_many(self, others):
         """
         A bit of a hack to accelerate unioning a collection of indexes.
         """
+        warnings.warn(
+            "DatetimeIndex.union_many is deprecated and will be removed in "
+            "a future version. Use obj.union instead.",
+            FutureWarning,
+            stacklevel=find_stack_level(),
+        )
+
         this = self
 
         for other in others:
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index b7d553707a91b..8b677bde2f7e2 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -2666,6 +2666,50 @@ def test_frame_from_dict_of_series_overlapping_monthly_period_indexes(self):
         exp = pd.period_range("1/1/1980", "1/1/2012", freq="M")
         tm.assert_index_equal(df.index, exp)
 
+    def test_frame_from_dict_with_mixed_tzaware_indexes(self):
+        # GH#44091
+        dti = date_range("2016-01-01", periods=3)
+
+        ser1 = Series(range(3), index=dti)
+        ser2 = Series(range(3), index=dti.tz_localize("UTC"))
+        ser3 = Series(range(3), index=dti.tz_localize("US/Central"))
+        ser4 = Series(range(3))
+
+        # no tz-naive, but we do have mixed tzs and a non-DTI
+        df1 = DataFrame({"A": ser2, "B": ser3, "C": ser4})
+        exp_index = Index(
+            list(ser2.index) + list(ser3.index) + list(ser4.index), dtype=object
+        )
+        tm.assert_index_equal(df1.index, exp_index)
+
+        df2 = DataFrame({"A": ser2, "C": ser4, "B": ser3})
+        exp_index3 = Index(
+            list(ser2.index) + list(ser4.index) + list(ser3.index), dtype=object
+        )
+        tm.assert_index_equal(df2.index, exp_index3)
+
+        df3 = DataFrame({"B": ser3, "A": ser2, "C": ser4})
+        exp_index3 = Index(
+            list(ser3.index) + list(ser2.index) + list(ser4.index), dtype=object
+        )
+        tm.assert_index_equal(df3.index, exp_index3)
+
+        df4 = DataFrame({"C": ser4, "B": ser3, "A": ser2})
+        exp_index4 = Index(
+            list(ser4.index) + list(ser3.index) + list(ser2.index), dtype=object
+        )
+        tm.assert_index_equal(df4.index, exp_index4)
+
+        # TODO: not clear if these raising is desired (no extant tests),
+        #  but this is de facto behavior 2021-12-22
+        msg = "Cannot join tz-naive with tz-aware DatetimeIndex"
+        with pytest.raises(TypeError, match=msg):
+            DataFrame({"A": ser2, "B": ser3, "C": ser4, "D": ser1})
+        with pytest.raises(TypeError, match=msg):
+            DataFrame({"A": ser2, "B": ser3, "D": ser1})
+        with pytest.raises(TypeError, match=msg):
+            DataFrame({"D": ser1, "A": ser2, "B": ser3})
+
 
 class TestDataFrameConstructorWithDtypeCoercion:
     def test_floating_values_integer_dtype(self):
@@ -2911,7 +2955,7 @@ def test_construction_from_ndarray_with_eadtype_mismatched_columns(self):
             DataFrame(arr2, columns=["foo", "bar"])
 
 
-def get1(obj):
+def get1(obj):  # TODO: make a helper in tm?
     if isinstance(obj, Series):
         return obj.iloc[0]
     else:
diff --git a/pandas/tests/indexes/datetimes/test_setops.py b/pandas/tests/indexes/datetimes/test_setops.py
index ae4ed04f8adac..7c2b3b7f4482d 100644
--- a/pandas/tests/indexes/datetimes/test_setops.py
+++ b/pandas/tests/indexes/datetimes/test_setops.py
@@ -26,6 +26,13 @@
 START, END = datetime(2009, 1, 1), datetime(2010, 1, 1)
 
 
+def test_union_many_deprecated():
+    dti = date_range("2016-01-01", periods=3)
+
+    with tm.assert_produces_warning(FutureWarning):
+        dti.union_many([dti, dti])
+
+
 class TestDatetimeIndexSetOps:
     tz = [
         None,